28:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 29:T5d2,LCM application They stand together again after a time that is a whole number of rounds for each of them, i.e. after the LCM of 6, 8, 10 and 14 minutes.

6 = 2 \times 3

8 = 2^{3}

10 = 2 \times 5

14 = 2 \times 7

. Taking the highest power of each prime, LCM

= 2^{3} \times 3 \times 5 \times 7 = 840

minutes. 840 minutes

= \frac{840}{60} = 14

hours. Hence they meet again at the starting position after 14 hours, so the correct option is (d).2a:T749,ल.स. का अनुप्रयोग वे तभी पुनः एक साथ होंगे जब बीता समय प्रत्येक के एक चक्कर के समय का पूर्ण गुणज हो, अर्थात 6, 8, 10 और 14 मिनट के ल.स. के बाद।

6 = 2 \times 3

8 = 2^{3}

10 = 2 \times 5

14 = 2 \times 7

। प्रत्येक अभाज्य की उच्चतम घात लेने पर, ल.स.

= 2^{3} \times 3 \times 5 \times 7 = 840

मिनट। 840 मिनट

= \frac{840}{60} = 14

घंटे। अतः वे 14 घंटे बाद प्रारंभिक स्थिति पर पुनः मिलेंगे, इसलिए सही विकल्प (d) है।2b:T458,Surface area of hemisphere A solid hemisphere shows two surfaces: the curved dome and the flat circular face.

Total surface area

= 2 π r^{2} + π r^{2} = 3 π r^{2}

. r=0.07 m =7 cm, and the options are in cm², so work in cm. TSA

= 3 \times \frac{22}{7} \times 7^{2} = 3 \times 22 \times 7 = 462

. Hence the total surface area is 462 cm², so the correct option is (d).2c:T5e0,अर्धगोले का पृष्ठीय क्षेत्रफल ठोस अर्धगोले में दो पृष्ठ होते हैं: वक्र पृष्ठ तथा समतल वृत्ताकार फलक।

कुल पृष्ठीय क्षेत्रफल

= 2 π r^{2} + π r^{2} = 3 π r^{2}

। r=0.07 m =7 cm, तथा विकल्प cm² में हैं, अतः cm में हल कीजिए। कुल पृष्ठीय क्षेत्रफल

= 3 \times \frac{22}{7} \times 7^{2} = 3 \times 22 \times 7 = 462

। अतः कुल पृष्ठीय क्षेत्रफल 462 cm² है, इसलिए सही विकल्प (d) है।2d:T4b9,LCM of numbers The smallest number divisible by all of them is their LCM. 5=5,

10 = 2 \times 5

49 = 7^{2}

28 = 2^{2} \times 7

. Take the highest power of every prime that appears:

2^{2} \times 5 \times 7^{2}

. LCM

= 4 \times 5 \times 49 = 980

. Checking the traps: 1040 and 900 are not divisible by 49, and 1006 is not divisible by 5. Hence the smallest such natural number is 980, so the correct option is (a).2e:T627,संख्याओं का ल.स. इन सभी से विभाज्य सबसे छोटी संख्या इनका ल.स. होती है। 5=5,

10 = 2 \times 5

49 = 7^{2}

28 = 2^{2} \times 7

। प्रत्येक अभाज्य की उच्चतम घात लीजिए:

2^{2} \times 5 \times 7^{2}

। ल.स.

= 4 \times 5 \times 49 = 980

। भ्रामक विकल्पों की जाँच: 1040 तथा 900, 49 से विभाज्य नहीं हैं और 1006, 5 से विभाज्य नहीं है। अतः अभीष्ट सबसे छोटी प्राकृत संख्या 980 है, इसलिए सही विकल्प (a) है।2f:T4cf,Profit percentage Let the selling price of one chair be S and its cost price be C. Gain on 150 chairs = selling price of 50 chairs, so 150S-150C=50S.

100 S = 150 C \Rightarrow \frac{S}{C} = \frac{3}{2}

; take S=3 and C=2. Profit

% = \frac{S - C}{C} \times 100 = \frac{3 - 2}{2} \times 100 = 50 %

. The gain is always measured on the cost price, so the answer is not

\frac{1}{3} \times 100

. Hence his profit percentage is

50 %

, so the correct option is (b).30:T625,लाभ प्रतिशत माना कि एक कुर्सी का विक्रय मूल्य S तथा क्रय मूल्य C है। 150 कुर्सियों पर लाभ = 50 कुर्सियों का विक्रय मूल्य, अतः 150S-150C=50S।

100 S = 150 C \Rightarrow \frac{S}{C} = \frac{3}{2}

; माना कि S=3 तथा C=2। लाभ

% = \frac{S - C}{C} \times 100 = \frac{3 - 2}{2} \times 100 = 50 %

। लाभ सदैव क्रय मूल्य पर मापा जाता है, अतः उत्तर

\frac{1}{3} \times 100

नहीं होगा। अतः उसका लाभ प्रतिशत

50 %

है, इसलिए सही विकल्प (b) है।31:T728,Compound interest ratio Let Shan get ₹S and Piyush get ₹P, so S+P=1612. Their amounts are equal:

S {(1 + \frac{8}{100})}^{19} = P {(1 + \frac{8}{100})}^{20}

. Dividing both sides by

{(1 + \frac{8}{100})}^{19}

gives

S = P (1 + \frac{8}{100})

\frac{S}{P} = \frac{27}{25}

, so the money is divided in the ratio 27:25, i.e. 27+25=52 parts. One part

= \frac{1612}{52} = 31

. Shan's share

= 27 \times 31 = 837

. Hence Rishi gave ₹837 to Shan, so the correct option is (b).32:T88a,चक्रवृद्धि ब्याज अनुपात माना कि शान को ₹S तथा पीयूष को ₹P मिले, अतः S+P=1612। दोनों का मिश्रधन समान है:

S {(1 + \frac{8}{100})}^{19} = P {(1 + \frac{8}{100})}^{20}

। दोनों पक्षों को

{(1 + \frac{8}{100})}^{19}

से भाग देने पर

S = P (1 + \frac{8}{100})

।

\frac{S}{P} = \frac{27}{25}

, अतः राशि 27:25 के अनुपात में बँटी, अर्थात कुल 27+25=52 भाग। एक भाग

= \frac{1612}{52} = 31

। शान का हिस्सा

= 27 \times 31 = 837

। अतः ऋषि ने शान को ₹837 दिए, इसलिए सही विकल्प (b) है।33:T5bc,Work and wages Take the total work as the LCM of 5, 8 and 6, i.e. 120 units. One day's work: A

= \frac{120}{5} = 24

, B

= \frac{120}{8} = 15

, C

= \frac{120}{6} = 20

units. Wages are shared in the ratio of work done, i.e. 24:15:20, a total of 59 parts. One part

= \frac{22774}{59} = 386

Difference of B's and C's shares

= (20 - 15) \times 386 = 5 \times 386 = 1930

. Hence the difference is ₹1,930, so the correct option is (a).34:T6d9,कार्य और मजदूरी कुल कार्य को 5, 8 और 6 का ल.स. अर्थात 120 इकाई मानिए। एक दिन का कार्य: A

= \frac{120}{5} = 24

, B

= \frac{120}{8} = 15

, C

= \frac{120}{6} = 20

इकाई। मजदूरी किए गए कार्य के अनुपात में बँटती है, अर्थात 24:15:20, कुल 59 भाग। एक भाग

= \frac{22774}{59} = 386

।

B तथा C के हिस्सों का अंतर

= (20 - 15) \times 386 = 5 \times 386 = 1930

। अतः अभीष्ट अंतर ₹1,930 है, इसलिए सही विकल्प (a) है।35:T5f4,HCF and LCM HCF =7, so LCM

= 126 \times 7 = 882

. Let the numbers be 7a and 7b with a and b coprime; then LCM

= 7 a b = 882 \Rightarrow a b = 126

. Their difference is

5 \times 7 = 35

, so

7 (a - b) = 35 \Rightarrow a - b = 5

. ab=126 with a-b=5 gives a=14 and b=9, which are coprime as required. Product

= 7 a \times 7 b = 49 \times 126 = 6174

. The same value follows from HCF

\times

LCM

= 7 \times 882 = 6174

. Hence the product of the two numbers is 6174, so the correct option is (b).36:T771,म.स. और ल.स. म.स. =7, अतः ल.स.

= 126 \times 7 = 882

। माना कि संख्याएँ 7a तथा 7b हैं, जहाँ a और b सह-अभाज्य हैं; तब ल.स.

= 7 a b = 882 \Rightarrow a b = 126

। उनका अंतर

5 \times 7 = 35

है, अतः

7 (a - b) = 35 \Rightarrow a - b = 5

। ab=126 तथा a-b=5 से a=14 और b=9 प्राप्त होते हैं, जो आवश्यकतानुसार सह-अभाज्य हैं। गुणनफल

= 7 a \times 7 b = 49 \times 126 = 6174

। यही मान म.स.

\times

ल.स.

= 7 \times 882 = 6174

से भी मिलता है। अतः दोनों संख्याओं का गुणनफल 6174 है, इसलिए सही विकल्प (b) है।37:T616,Successive percentage change Take the original price as 100. A fall of

x %

multiplies the price by

(1 - \frac{x}{100})

and a rise by

(1 + \frac{x}{100})

Final price

= 100 \times 0.6 \times 0.7 \times 0.9 \times 1.4 = 52.92

. Change =52.92-100=-47.08 on a base of 100. Percentages of different months cannot be added, which is why

- 40 - 30 - 10 + 40 = - 40 %

is wrong. Hence the price decreases by

47.08 %

, so the correct option is (a).38:T766,क्रमिक प्रतिशत परिवर्तन मूल कीमत को 100 मानिए।

x %

की कमी कीमत को

(1 - \frac{x}{100})

से तथा वृद्धि

(1 + \frac{x}{100})

से गुणा करती है।

अंतिम कीमत

= 100 \times 0.6 \times 0.7 \times 0.9 \times 1.4 = 52.92

। परिवर्तन =52.92-100=-47.08, आधार 100 पर। भिन्न महीनों के प्रतिशत जोड़े नहीं जा सकते, इसीलिए

- 40 - 30 - 10 + 40 = - 40 %

लेना गलत है। अतः कीमत में

47.08 %

की कमी होती है, इसलिए सही विकल्प (a) है।39:T5bb,SI and CI difference For 2 years SI =42, so the interest of one year

= \frac{42}{2} = 21

. For 2 years, CI - SI is exactly one year's interest on the first year's interest. 63-42=21, so

21 \times \frac{R}{100} = 21 \Rightarrow R = 100

. Now

S I = \frac{P \times R \times T}{100}

gives

\frac{P \times 100 \times 2}{100} = 42 \Rightarrow 2 P = 42

. P=21. Check: at

100 %

the amount grows

21 \to 42 \to 84

, so CI =84-21=63, as given. Hence the principal is ₹21, so the correct option is (a).3a:T79b,साधारण और चक्रवृद्धि ब्याज का अंतर 2 वर्ष का साधारण ब्याज =42 है, अतः एक वर्ष का ब्याज

= \frac{42}{2} = 21

। 2 वर्ष में चक्रवृद्धि ब्याज - साधारण ब्याज ठीक पहले वर्ष के ब्याज पर एक वर्ष का ब्याज होता है। 63-42=21, अतः

21 \times \frac{R}{100} = 21 \Rightarrow R = 100

। अब

S I = \frac{P \times R \times T}{100}

से

\frac{P \times 100 \times 2}{100} = 42 \Rightarrow 2 P = 42

। P=21। जाँच:

100 %

दर पर मिश्रधन

21 \to 42 \to 84

बढ़ता है, अतः चक्रवृद्धि ब्याज =84-21=63, जो दिया गया है। अतः मूलधन ₹21 है, इसलिए सही विकल्प (a) है।3b:T46f,Alligation of prices Rule of alligation:

\frac{cheaper quantity}{dearer quantity} = \frac{dearer price - mean price}{mean price - cheaper price}

= \frac{285 - 195}{195 - 165} = \frac{90}{30} = \frac{3}{1}

. The mean 195 lies much nearer to 165, so the cheaper variety must be the larger share, which 3:1 satisfies. Hence the two varieties must be mixed in the ratio 3:1, so the correct option is (b).3c:T62c,कीमतों का मिश्रण मिश्रण नियम:

\frac{सस्ती किस्म की मात्रा}{महँगी किस्म की मात्रा} = \frac{महँगी कीमत - औसत कीमत}{औसत कीमत - सस्ती कीमत}

।

= \frac{285 - 195}{195 - 165} = \frac{90}{30} = \frac{3}{1}

। औसत 195, कीमत 165 के अधिक निकट है, अतः सस्ती किस्म की मात्रा अधिक होनी चाहिए, जो 3:1 से सिद्ध होता है। अतः दोनों किस्मों को 3:1 के अनुपात में मिलाना होगा, इसलिए सही विकल्प (b) है।3d:T4a5,Marked price and discount A discount of

20 %

means the pair was paid for at

80 %

of the marked price of the pair.

\frac{80}{100} \times M P_{pair} = 1820

M P_{pair} = \frac{1820 \times 100}{80} = 2275

. Both articles carry the same marked price, so the MP of one

= \frac{2275}{2} = 1137.50

. Hence the marked price of an article is ₹1,137.50, so the correct option is (a).3e:T593,अंकित मूल्य और छूट

20 %

की छूट का अर्थ है कि जोड़े का भुगतान उसके अंकित मूल्य के

80 %

पर हुआ।

\frac{80}{100} \times M P = 1820

(जोड़े के लिए)।

M P = \frac{1820 \times 100}{80} = 2275

(जोड़े का)। दोनों वस्तुओं का अंकित मूल्य समान है, अतः एक वस्तु का

M P = \frac{2275}{2} = 1137.50

। अतः एक वस्तु का अंकित मूल्य ₹1,137.50 है, इसलिए सही विकल्प (a) है।3f:T498,Boat and stream Let the speed of the boat in still water be x km/h; then downstream =x+9 and upstream =x-9.

\frac{28}{x + 9} + \frac{20}{x - 9} = 8

. 28(x-9)+20(x+9)=8(x+9)(x-9).

48 x - 72 = 8 x^{2} - 648

8 x^{2} - 48 x - 576 = 0 \Rightarrow x^{2} - 6 x - 72 = 0

. (x-12)(x+6)=0, and a speed cannot be negative, so x=12. Hence the speed of the boat in still water is 12 km/h, so the correct option is (c).40:T58c,नाव और धारा माना कि शांत जल में नाव की चाल x km/h है; तब अनुप्रवाह चाल =x+9 तथा ऊर्ध्वप्रवाह चाल =x-9।

\frac{28}{x + 9} + \frac{20}{x - 9} = 8

। 28(x-9)+20(x+9)=8(x+9)(x-9)।

48 x - 72 = 8 x^{2} - 648

।

8 x^{2} - 48 x - 576 = 0 \Rightarrow x^{2} - 6 x - 72 = 0

। (x-12)(x+6)=0, और चाल ऋणात्मक नहीं हो सकती, अतः x=12। अतः शांत जल में नाव की चाल 12 km/h है, इसलिए सही विकल्प (c) है।41:T500,Time and work (men-days) The job is fixed, so men

\times

days stays constant:

M_{1} D_{1} = M_{2} D_{2}

80 \times 100 = M_{2} \times 25

M_{2} = \frac{8000}{25} = 320

men are needed to finish it in 25 days. The question asks for the extra men: 320-80=240. Hence 240 more men should be employed, so the correct option is (d).42:T654,समय और कार्य (पुरुष-दिन) कार्य नियत है, अतः पुरुष

\times

दिन अचर रहता है:

M_{1} D_{1} = M_{2} D_{2}

।

80 \times 100 = M_{2} \times 25

।

M_{2} = \frac{8000}{25} = 320

पुरुष 25 दिन में कार्य पूरा करने के लिए आवश्यक हैं। प्रश्न में अतिरिक्त पुरुष पूछे गए हैं: 320-80=240। अतः 240 और पुरुषों को लगाया जाना चाहिए, इसलिए सही विकल्प (d) है।1e:["$","$L28",null,{"mode":"exam","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":8641,"n":41,"subject":"Elementary Mathematics","stem":"Vijay invests a sum of ₹5400 and Mohan invests a sum of ₹9400 at the same rate of simple interest per annum. If, at the end of 6 years, Mohan gets ₹600 more interest than Vijay, then find the rate of interest per annum (in percentage).","stemHi":"विजय ₹5400 की राशि तथा मोहन ₹9400 की राशि समान वार्षिक साधारण ब्याज दर पर निवेश करते हैं। यदि 6 वर्ष के अंत में मोहन को विजय से ₹600 अधिक ब्याज मिलता है, तो वार्षिक ब्याज दर (प्रतिशत में) ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"3.5","textHi":null,"imageUrl":null},{"key":"b","text":"4.5","textHi":null,"imageUrl":null},{"key":"c","text":"1.5","textHi":null,"imageUrl":null},{"key":"d","text":"2.5","textHi":null,"imageUrl":null}],"correct":"d","sol":"Simple interest\nFormula:

S I = \frac{P \times R \times T}{100}

.\nBoth sums run for the same T=6 years at the same rate R, so the whole gap of ₹600 comes from the gap in principal.\nDifference of principals =9400-5400=4000.\nSo

\frac{4000 \times R \times 6}{100} = 600

.\n

240 R = 600 \Rightarrow R = 2.5

.\nHence the rate of interest is

2.5 %

per annum, so the correct option is (d).","solHi":"साधारण ब्याज\nसूत्र:

S I = \frac{P \times R \times T}{100}

।\nदोनों राशियाँ समान समय T=6 वर्ष के लिए समान दर R पर लगी हैं, अतः ₹600 का पूरा अंतर केवल मूलधन के अंतर से आया है।\nमूलधनों का अंतर =9400-5400=4000।\nअतः

\frac{4000 \times R \times 6}{100} = 600

।\n

240 R = 600 \Rightarrow R = 2.5

।\nअतः वार्षिक ब्याज दर

2.5 %

है, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":8642,"n":42,"subject":"Elementary Mathematics","stem":"Four people move along the circumference of a park. They complete one round in 6 minutes, 8 minutes, 10 minutes and 14 minutes, respectively. Since they started together, after how many hours will they meet again at the starting position?","stemHi":"चार व्यक्ति एक पार्क की परिधि के अनुदिश चलते हैं। वे एक चक्कर क्रमशः 6 मिनट, 8 मिनट, 10 मिनट और 14 मिनट में पूरा करते हैं। एक साथ चलना आरंभ करने के बाद, वे कितने घंटे बाद पुनः प्रारंभिक स्थिति पर मिलेंगे?","context":null,"contextHi":null,"options":[{"key":"a","text":"18","textHi":null,"imageUrl":null},{"key":"b","text":"15","textHi":null,"imageUrl":null},{"key":"c","text":"12","textHi":null,"imageUrl":null},{"key":"d","text":"14","textHi":null,"imageUrl":null}],"correct":"d","sol":"$29","solHi":"$2a","pos":2,"neg":0.25},{"id":8643,"n":43,"subject":"Elementary Mathematics","stem":"The greatest number, which divides 1163 and 2214 to leave 15 and 82 respectively as remainders, is:","stemHi":"वह सबसे बड़ी संख्या, जो 1163 और 2214 को विभाजित करने पर क्रमशः 15 और 82 शेषफल छोड़ती है, है:","context":null,"contextHi":null,"options":[{"key":"a","text":"173","textHi":null,"imageUrl":null},{"key":"b","text":"169","textHi":null,"imageUrl":null},{"key":"c","text":"159","textHi":null,"imageUrl":null},{"key":"d","text":"164","textHi":null,"imageUrl":null}],"correct":"d","sol":"HCF with remainders\nIf the divisor leaves remainder 15 in 1163, it divides 1163-15=1148 exactly.\nIn the same way it divides 2214-82=2132 exactly.\nSo the required number is the HCF of 1148 and 2132.\n

2132 = 1148 \times 1 + 984

;

1148 = 984 \times 1 + 164

;

984 = 164 \times 6 + 0

.\nSo HCF =164, and 164 is larger than both remainders, as a divisor must be.\nHence the greatest such number is 164, so the correct option is (d).","solHi":"शेषफल सहित म.स.\nयदि भाजक 1163 में शेषफल 15 छोड़ता है, तो वह 1163-15=1148 को पूर्णतः विभाजित करता है।\nइसी प्रकार वह 2214-82=2132 को भी पूर्णतः विभाजित करता है।\nअतः अभीष्ट संख्या 1148 और 2132 का म.स. है।\n

2132 = 1148 \times 1 + 984

;

1148 = 984 \times 1 + 164

;

984 = 164 \times 6 + 0

।\nअतः म.स. =164, और यह दोनों शेषफलों से बड़ा है, जो भाजक के लिए आवश्यक है।\nअतः अभीष्ट सबसे बड़ी संख्या 164 है, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":8644,"n":44,"subject":"Elementary Mathematics","stem":"A man's monthly salary increased from ₹42,000 to ₹57,000. What is the percentage (rounded off to 1 decimal place) increase in his monthly salary?","stemHi":"एक व्यक्ति का मासिक वेतन ₹42,000 से बढ़कर ₹57,000 हो गया। उसके मासिक वेतन में हुई प्रतिशत वृद्धि (1 दशमलव स्थान तक पूर्णांकित) कितनी है?","context":null,"contextHi":null,"options":[{"key":"a","text":"35.7%","textHi":null,"imageUrl":null},{"key":"b","text":"55.7%","textHi":null,"imageUrl":null},{"key":"c","text":"37.5%","textHi":null,"imageUrl":null},{"key":"d","text":"57.5%","textHi":null,"imageUrl":null}],"correct":"a","sol":"Percentage increase\nIncrease in salary =57000-42000=15000.\nPercentage increase

= \frac{increase}{original salary} \times 100

.\n

= \frac{15000}{42000} \times 100 = \frac{250}{7} = 35.714 \dots

\nRounded off to one decimal place this is

35.7 %

.\nThe base is always the original salary ₹42,000; dividing by the new ₹57,000 gives the trap value

26.3 %

.\nHence the correct option is (a).","solHi":"प्रतिशत वृद्धि\nवेतन में वृद्धि =57000-42000=15000।\nप्रतिशत वृद्धि

= \frac{वृद्धि}{मूल वेतन} \times 100

।\n

= \frac{15000}{42000} \times 100 = \frac{250}{7} = 35.714 \dots

\nएक दशमलव स्थान तक पूर्णांकित करने पर यह

35.7 %

है।\nआधार सदैव मूल वेतन ₹42,000 होता है; नए वेतन ₹57,000 से भाग देने पर भ्रामक मान

26.3 %

मिलता है।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":8645,"n":45,"subject":"Elementary Mathematics","stem":"Find the total surface area of a solid hemisphere of radius 0.07 m . (Use

π = \frac{22}{7}

)","stemHi":"0.07 m त्रिज्या वाले एक ठोस अर्धगोले का कुल पृष्ठीय क्षेत्रफल ज्ञात कीजिए। (

π = \frac{22}{7}

का प्रयोग कीजिए)","context":null,"contextHi":null,"options":[{"key":"a","text":"442 cm²","textHi":null,"imageUrl":null},{"key":"b","text":"472 cm²","textHi":null,"imageUrl":null},{"key":"c","text":"452 cm²","textHi":null,"imageUrl":null},{"key":"d","text":"462 cm²","textHi":null,"imageUrl":null}],"correct":"d","sol":"$2b","solHi":"$2c","pos":2,"neg":0.25},{"id":8646,"n":46,"subject":"Elementary Mathematics","stem":"The smallest natural number which is divisible by 5, 10, 49 and 28 is:","stemHi":"वह सबसे छोटी प्राकृत संख्या, जो 5, 10, 49 और 28 से विभाज्य है, है:","context":null,"contextHi":null,"options":[{"key":"a","text":"980","textHi":null,"imageUrl":null},{"key":"b","text":"1040","textHi":null,"imageUrl":null},{"key":"c","text":"900","textHi":null,"imageUrl":null},{"key":"d","text":"1006","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2d","solHi":"$2e","pos":2,"neg":0.25},{"id":8647,"n":47,"subject":"Elementary Mathematics","stem":"Tushar sold 150 chairs and had a gain equal to the selling price of 50 chairs. What is his profit percentage ?","stemHi":"तुषार ने 150 कुर्सियाँ बेचीं और उसे 50 कुर्सियों के विक्रय मूल्य के बराबर लाभ हुआ। उसका लाभ प्रतिशत कितना है?","context":null,"contextHi":null,"options":[{"key":"a","text":"60%","textHi":null,"imageUrl":null},{"key":"b","text":"50 %","textHi":null,"imageUrl":null},{"key":"c","text":"55%","textHi":null,"imageUrl":null},{"key":"d","text":"45%","textHi":null,"imageUrl":null}],"correct":"b","sol":"$2f","solHi":"$30","pos":2,"neg":0.25},{"id":8648,"n":48,"subject":"Elementary Mathematics","stem":"Rishi has ₹1612 with him. He divided it amongst his sons Shan and Piyush and asked them to invest it at 8% rate of interest compounded annually. It was seen that Shan and Piyush got same amount after 19 and 20 years respectively. How much (in ₹) did Rishi give to Shan ?","stemHi":"ऋषि के पास ₹1612 हैं। उसने इसे अपने पुत्रों शान और पीयूष में बाँट दिया और उनसे कहा कि वे इसे 8% वार्षिक चक्रवृद्धि ब्याज दर पर निवेश करें। यह देखा गया कि शान और पीयूष को क्रमशः 19 और 20 वर्ष बाद समान मिश्रधन प्राप्त हुआ। ऋषि ने शान को कितनी राशि (₹ में) दी थी?","context":null,"contextHi":null,"options":[{"key":"a","text":"687","textHi":null,"imageUrl":null},{"key":"b","text":"837","textHi":null,"imageUrl":null},{"key":"c","text":"875","textHi":null,"imageUrl":null},{"key":"d","text":"775","textHi":null,"imageUrl":null}],"correct":"b","sol":"$31","solHi":"$32","pos":2,"neg":0.25},{"id":8649,"n":49,"subject":"Elementary Mathematics","stem":"A, B and C working separately can do a piece of work in 5, 8 and 6 days, respectively. If they all work together and earn ₹22,774 for the whole work, then find the difference between the shares of B and C.","stemHi":"A, B और C अलग-अलग कार्य करते हुए एक कार्य को क्रमशः 5, 8 और 6 दिन में पूरा कर सकते हैं। यदि वे सभी मिलकर कार्य करते हैं और पूरे कार्य के लिए ₹22,774 कमाते हैं, तो B और C के हिस्सों के बीच अंतर ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"₹1,930","textHi":null,"imageUrl":null},{"key":"b","text":"₹1,560","textHi":null,"imageUrl":null},{"key":"c","text":"₹1,840","textHi":null,"imageUrl":null},{"key":"d","text":"₹2,010","textHi":null,"imageUrl":null}],"correct":"a","sol":"$33","solHi":"$34","pos":2,"neg":0.25},{"id":8650,"n":50,"subject":"Elementary Mathematics","stem":"A shopkeeper bought an article for ₹500. At what price (in ₹) should he sell the article to make 24% profit ?","stemHi":"एक दुकानदार ने एक वस्तु ₹500 में खरीदी। 24% लाभ कमाने के लिए उसे वह वस्तु किस मूल्य (₹ में) पर बेचनी चाहिए?","context":null,"contextHi":null,"options":[{"key":"a","text":"632","textHi":null,"imageUrl":null},{"key":"b","text":"608","textHi":null,"imageUrl":null},{"key":"c","text":"380","textHi":null,"imageUrl":null},{"key":"d","text":"620","textHi":null,"imageUrl":null}],"correct":"d","sol":"Selling price from profit\nFormula:

S P = C P \times (1 + \frac{profit %}{100})

.\n

S P = 500 \times (1 + \frac{24}{100}) = 500 \times \frac{124}{100}

.\n

S P = 5 \times 124 = 620

.\nHence he should sell the article for ₹620, so the correct option is (d).","solHi":"लाभ से विक्रय मूल्य\nसूत्र:

S P = C P \times (1 + \frac{लाभ %}{100})

।\n

S P = 500 \times (1 + \frac{24}{100}) = 500 \times \frac{124}{100}

।\n

S P = 5 \times 124 = 620

।\nअतः उसे वस्तु ₹620 में बेचनी चाहिए, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":8651,"n":51,"subject":"Elementary Mathematics","stem":"The LCM of two numbers is 126 times their HCF. If their HCF is 7 and the difference between the two numbers is five times the HCF, then the product of the two numbers is:","stemHi":"दो संख्याओं का ल.स. उनके म.स. का 126 गुना है। यदि उनका म.स. 7 है और दोनों संख्याओं का अंतर म.स. का पाँच गुना है, तो दोनों संख्याओं का गुणनफल है:","context":null,"contextHi":null,"options":[{"key":"a","text":"1476","textHi":null,"imageUrl":null},{"key":"b","text":"6174","textHi":null,"imageUrl":null},{"key":"c","text":"7164","textHi":null,"imageUrl":null},{"key":"d","text":"6471","textHi":null,"imageUrl":null}],"correct":"b","sol":"$35","solHi":"$36","pos":2,"neg":0.25},{"id":8652,"n":52,"subject":"Elementary Mathematics","stem":"The average weight of Anwar, Amit and Gopal is 46 kg . If the average weight of Anwar and Amit be 39 kg and that of Amit and Gopal be 44 kg , then the weight of Amit (in kg) is:","stemHi":"Anwar, Amit और Gopal का औसत भार 46 kg है। यदि Anwar और Amit का औसत भार 39 kg है तथा Amit और Gopal का औसत भार 44 kg है, तो Amit का भार (kg में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"43","textHi":null,"imageUrl":null},{"key":"b","text":"38","textHi":null,"imageUrl":null},{"key":"c","text":"48","textHi":null,"imageUrl":null},{"key":"d","text":"28","textHi":null,"imageUrl":null}],"correct":"d","sol":"Average of weights\nSum of the three weights

= 3 \times 46 = 138

kg.\n $\"figure\"/$ \nAnwar + Amit

= 2 \times 39 = 78

, so Gopal =138-78=60 kg.\nAmit + Gopal

= 2 \times 44 = 88

, so Anwar =138-88=50 kg.\nAmit =138-60-50=28 kg.\nHence the weight of Amit is 28 kg, so the correct option is (d).","solHi":"भार का औसत\nतीनों के भारों का योग

= 3 \times 46 = 138

kg।\n $\"figure\"/$ \nAnwar + Amit

= 2 \times 39 = 78

, अतः Gopal =138-78=60 kg।\nAmit + Gopal

= 2 \times 44 = 88

, अतः Anwar =138-88=50 kg।\nAmit =138-60-50=28 kg।\nअतः Amit का भार 28 kg है, इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":8653,"n":53,"subject":"Elementary Mathematics","stem":"The price of fuel decreases by 40%, 30% and 10% in three successive months, but increases by 40% in the fourth month. What is the percentage increase/decrease in the price of fuel in the fourth month as compared to its original price?","stemHi":"ईंधन की कीमत तीन क्रमागत महीनों में 40%, 30% और 10% घटती है, किंतु चौथे महीने में 40% बढ़ जाती है। मूल कीमत की तुलना में चौथे महीने में ईंधन की कीमत में कितने प्रतिशत की वृद्धि/कमी हुई?","context":null,"contextHi":null,"options":[{"key":"a","text":"Decreases by 47.08%","textHi":"47.08% की कमी","imageUrl":null},{"key":"b","text":"Decreases by 43.81%","textHi":"43.81% की कमी","imageUrl":null},{"key":"c","text":"Increases by 49.94%","textHi":"49.94% की वृद्धि","imageUrl":null},{"key":"d","text":"Increases by 45.65%","textHi":"45.65% की वृद्धि","imageUrl":null}],"correct":"a","sol":"$37","solHi":"$38","pos":2,"neg":0.25},{"id":8654,"n":54,"subject":"Elementary Mathematics","stem":"If at same rate of interest, in 2 years, the simple interest is ₹42 and compound interest is ₹63, then what is the principal (in ₹)?","stemHi":"यदि समान ब्याज दर पर, 2 वर्ष में साधारण ब्याज ₹42 और चक्रवृद्धि ब्याज ₹63 है, तो मूलधन (₹ में) कितना है?","context":null,"contextHi":null,"options":[{"key":"a","text":"21","textHi":null,"imageUrl":null},{"key":"b","text":"14","textHi":null,"imageUrl":null},{"key":"c","text":"16","textHi":null,"imageUrl":null},{"key":"d","text":"25","textHi":null,"imageUrl":null}],"correct":"a","sol":"$39","solHi":"$3a","pos":2,"neg":0.25},{"id":8655,"n":55,"subject":"Elementary Mathematics","stem":"In what ratio must a grocer mix two varieties of rice costing ₹165 and ₹285 per kg, respectively, to get a mixture of rice worth ₹195 per kg ?","stemHi":"एक पंसारी को ₹165 और ₹285 प्रति kg कीमत वाली चावल की दो किस्मों को किस अनुपात में मिलाना चाहिए, ताकि ₹195 प्रति kg कीमत वाला चावल का मिश्रण प्राप्त हो?","context":null,"contextHi":null,"options":[{"key":"a","text":"7 : 4","textHi":null,"imageUrl":null},{"key":"b","text":"3 : 1","textHi":null,"imageUrl":null},{"key":"c","text":"5 : 2","textHi":null,"imageUrl":null},{"key":"d","text":"9 : 5","textHi":null,"imageUrl":null}],"correct":"b","sol":"$3b","solHi":"$3c","pos":2,"neg":0.25},{"id":8656,"n":56,"subject":"Elementary Mathematics","stem":"A train 240 m long is running at a speed of

88 km / h

. In what time will it pass a man who is running at a speed of

16 km / h

in the same direction ?","stemHi":"240 m लंबी एक ट्रेन

88 km / h

की चाल से चल रही है। वह उसी दिशा में

16 km / h

की चाल से दौड़ रहे एक व्यक्ति को कितने समय में पार करेगी?","context":null,"contextHi":null,"options":[{"key":"a","text":"27 seconds","textHi":"27 सेकंड","imageUrl":null},{"key":"b","text":"12 seconds","textHi":"12 सेकंड","imageUrl":null},{"key":"c","text":"23 seconds","textHi":"23 सेकंड","imageUrl":null},{"key":"d","text":"9 seconds","textHi":"9 सेकंड","imageUrl":null}],"correct":"b","sol":"Relative speed\nThe man runs in the same direction as the train, so use the relative speed =88-16=72 km/h.\n72 km/h

= 72 \times \frac{5}{18} = 20

m/s.\nA train passes a man when it covers its own length, 240 m, at this relative speed.\nTime

= \frac{length}{relative speed} = \frac{240}{20} = 12

seconds.\nHence the train passes him in 12 seconds, so the correct option is (b).","solHi":"सापेक्ष चाल\nव्यक्ति ट्रेन की ही दिशा में दौड़ रहा है, अतः सापेक्ष चाल =88-16=72 km/h लीजिए।\n72 km/h

= 72 \times \frac{5}{18} = 20

m/s।\nट्रेन व्यक्ति को तब पार करती है जब वह इसी सापेक्ष चाल से अपनी लंबाई 240 m तय कर लेती है।\nसमय

= \frac{लंबाई}{सापेक्ष चाल} = \frac{240}{20} = 12

सेकंड।\nअतः ट्रेन उसे 12 सेकंड में पार कर लेती है, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.25},{"id":8657,"n":57,"subject":"Elementary Mathematics","stem":"Find the fourth proportional of 4, 12, and 20.","stemHi":"4, 12 और 20 का चतुर्थानुपाती ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"80","textHi":null,"imageUrl":null},{"key":"b","text":"60","textHi":null,"imageUrl":null},{"key":"c","text":"28","textHi":null,"imageUrl":null},{"key":"d","text":"30","textHi":null,"imageUrl":null}],"correct":"b","sol":"Fourth proportional\nIf x is the fourth proportional of a, b, c then a:b=c:x.\n

4 : 12 = 20 : x \Rightarrow 4 x = 12 \times 20

.\n

x = \frac{240}{4} = 60

.\nHence the fourth proportional is 60, so the correct option is (b).","solHi":"चतुर्थानुपाती\nयदि x, संख्याओं a, b, c का चतुर्थानुपाती है, तो a:b=c:x।\n

4 : 12 = 20 : x \Rightarrow 4 x = 12 \times 20

।\n

x = \frac{240}{4} = 60

।\nअतः चतुर्थानुपाती 60 है, इसलिए सही विकल्प (b) है।","pos":2,"neg":0.25},{"id":8658,"n":58,"subject":"Elementary Mathematics","stem":"A pair of articles was bought for ₹1,820 at a discount of 20%, and marked price of each article is same. What is the marked price (in ₹) of an article ?","stemHi":"वस्तुओं का एक जोड़ा 20% की छूट पर ₹1,820 में खरीदा गया, और प्रत्येक वस्तु का अंकित मूल्य समान है। एक वस्तु का अंकित मूल्य (₹ में) कितना है?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹1,137.50","textHi":null,"imageUrl":null},{"key":"b","text":"₹1,371.50","textHi":null,"imageUrl":null},{"key":"c","text":"₹1,173.50","textHi":null,"imageUrl":null},{"key":"d","text":"₹1,731.50","textHi":null,"imageUrl":null}],"correct":"a","sol":"$3d","solHi":"$3e","pos":2,"neg":0.25},{"id":8659,"n":59,"subject":"Elementary Mathematics","stem":"The speed of a stream is

9 km / h

. A boat can go 28 km downstream and 20 km upstream in 8 hours. What is the speed (in

km / h

) of the boat in still water?","stemHi":"एक धारा की चाल

9 km / h

है। एक नाव 8 घंटे में 28 km अनुप्रवाह और 20 km ऊर्ध्वप्रवाह जा सकती है। शांत जल में नाव की चाल (

km / h

में) कितनी है?","context":null,"contextHi":null,"options":[{"key":"a","text":"14","textHi":null,"imageUrl":null},{"key":"b","text":"9","textHi":null,"imageUrl":null},{"key":"c","text":"12","textHi":null,"imageUrl":null},{"key":"d","text":"6","textHi":null,"imageUrl":null}],"correct":"c","sol":"$3f","solHi":"$40","pos":2,"neg":0.25},{"id":8660,"n":60,"subject":"Elementary Mathematics","stem":"80 men can construct a small footpath in 100 days. How many more men should be employed if the job is to be finished in 25 days?","stemHi":"80 पुरुष एक छोटा फुटपाथ 100 दिन में बना सकते हैं। यदि कार्य को 25 दिन में समाप्त करना है, तो कितने और पुरुषों को लगाया जाना चाहिए?","context":null,"contextHi":null,"options":[{"key":"a","text":"250","textHi":null,"imageUrl":null},{"key":"b","text":"220","textHi":null,"imageUrl":null},{"key":"c","text":"210","textHi":null,"imageUrl":null},{"key":"d","text":"240","textHi":null,"imageUrl":null}],"correct":"d","sol":"$41","solHi":"$42","pos":2,"neg":0.25}],"test":{"slug":"ssc-gd-constable--13-feb-2025-shift-2-maths","title":"SSC GD Constable 13 February 2025 Shift-2 — Elementary Mathematics Sectional Test","examName":"SSC GD","paperLabel":"13 February 2025 · Shift 2","sectionSubject":"Elementary Mathematics","durationMinutes":15,"format":"sectional_test"}}]