28:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 29:T71b,Compound interest, equal amounts Let Varun get V and Ashish get A. Both reach the SAME amount, Varun in 13 years and Ashish in 14 years at

10 %

compounded annually.

V {(\frac{11}{10})}^{13} = A {(\frac{11}{10})}^{14}

\frac{V}{A} = {(\frac{11}{10})}^{14 - 13} = \frac{11}{10}

Ashish has one extra year to grow, so his share must be the smaller one: Varun : Ashish =11:10.

11+10=21 units =1218, so 1 unit

= \frac{1218}{21} = 58

Ashish's share

= 10 \times 58 = 580

So Raj gave Ashish ₹580 and the correct option is (d).2a:T8de,चक्रवृद्धि ब्याज, समान मिश्रधन माना कि Varun को V तथा Ashish को A मिलता है। दोनों को समान मिश्रधन प्राप्त होता है, Varun को 13 वर्ष में तथा Ashish को 14 वर्ष में,

10 %

वार्षिक चक्रवृद्धि दर पर।

V {(\frac{11}{10})}^{13} = A {(\frac{11}{10})}^{14}

\frac{V}{A} = {(\frac{11}{10})}^{14 - 13} = \frac{11}{10}

Ashish को बढ़ने के लिए एक वर्ष अधिक मिलता है, अतः उसका भाग छोटा होगा: Varun : Ashish =11:10।

11+10=21 इकाई =1218, अतः 1 इकाई

= \frac{1218}{21} = 58

Ashish का भाग

= 10 \times 58 = 580

अतः Raj ने Ashish को ₹580 दिए और इसलिए सही विकल्प (d) है।2b:T645,LCM by prime factorisation Break every number into prime factors first.

36 = 2^{2} \times 3^{2}

and

30 = 2 \times 3 \times 5

114 = 2 \times 3 \times 19

and

380 = 2^{2} \times 5 \times 19

The LCM keeps the HIGHEST power of each prime that appears:

2^{2}

3^{2}

, 5 and 19. LCM

= 4 \times 9 \times 5 \times 19 = 3420

So the correct option is (b).2c:T738,अभाज्य गुणनखंड से ल.स. सबसे पहले प्रत्येक संख्या के अभाज्य गुणनखंड कीजिए।

36 = 2^{2} \times 3^{2}

तथा

30 = 2 \times 3 \times 5

114 = 2 \times 3 \times 19

तथा

380 = 2^{2} \times 5 \times 19

ल.स. में प्रत्येक अभाज्य की उच्चतम घात ली जाती है:

2^{2}

3^{2}

, 5 तथा 19। ल.स.

= 4 \times 9 \times 5 \times 19 = 3420

इसलिए सही विकल्प (b) है।2d:T6eb,Work done in rotation Take the total work as the LCM of 22, 24 and 33, that is 264 units. One day's work: A

= \frac{264}{22} = 12

, B

= \frac{264}{24} = 11

, C

= \frac{264}{33} = 8

units. The turn order is A, C, B, so one cycle of 3 days does 12+8+11=31 units.

8 cycles =24 days do

8 \times 31 = 248

units, leaving 264-248=16 units. Day 25 belongs to A, who does 12 units; work left =16-12=4 units. Day 26 belongs to C, who needs

\frac{4}{8} = \frac{1}{2}

day for the last 4 units. Total time

= 24 + 1 + \frac{1}{2} = 25 \frac{1}{2}

days So the correct option is (c).2e:T8c7,क्रम से किया गया कार्य कुल कार्य को 22, 24 और 33 का ल.स., अर्थात् 264 इकाई मानिए। एक दिन का कार्य: A

= \frac{264}{22} = 12

, B

= \frac{264}{24} = 11

, C

= \frac{264}{33} = 8

इकाई। कार्य का क्रम A, C, B है, अतः 3 दिन के एक चक्र में 12+8+11=31 इकाई कार्य होता है।

8 चक्र =24 दिन में

8 \times 31 = 248

इकाई कार्य होता है, शेष 264-248=16 इकाई। 25वाँ दिन A का है, वह 12 इकाई करता है; शेष कार्य =16-12=4 इकाई। 26वाँ दिन C का है, अंतिम 4 इकाई के लिए उसे

\frac{4}{8} = \frac{1}{2}

दिन चाहिए। कुल समय

= 24 + 1 + \frac{1}{2} = 25 \frac{1}{2}

दिन इसलिए सही विकल्प (c) है।2f:T53a,SI and CI difference For 2 years the two interests differ only because compound interest also pays interest on the first year's interest. Simple interest of one year

= \frac{40}{2} = 20

Difference =50-40=10, and this 10 is exactly one year's interest on that 20.

\frac{20 \times R}{100} = 10

, so

R = 50 %

Principal

= \frac{100 \times S I}{R \times T} = \frac{100 \times 40}{50 \times 2} = 40

So the principal is ₹40 and the correct option is (a).30:T6c9,साधारण और चक्रवृद्धि ब्याज का अंतर 2 वर्षों में दोनों ब्याजों में अंतर केवल इसलिए आता है क्योंकि चक्रवृद्धि ब्याज में पहले वर्ष के ब्याज पर भी ब्याज मिलता है। एक वर्ष का साधारण ब्याज

= \frac{40}{2} = 20

अंतर =50-40=10, और यह 10 उसी 20 पर एक वर्ष का ब्याज है।

\frac{20 \times R}{100} = 10

, अतः

R = 50 %

मूलधन

= \frac{100 \times S I}{R \times T} = \frac{100 \times 40}{50 \times 2} = 40

अतः मूलधन ₹40 है और इसलिए सही विकल्प (a) है।31:T62f,LCM by prime factorisation Write each number as a product of primes.

51 = 3 \times 17

and

18 = 2 \times 3^{2}

432 = 2^{4} \times 3^{3}

and

144 = 2^{4} \times 3^{2}

The LCM takes the highest power of every prime:

2^{4} \times 3^{3} \times 17

LCM

= 16 \times 27 \times 17 = 432 \times 17 = 7344

So the correct option is (a).32:T74a,अभाज्य गुणनखंड से ल.स. प्रत्येक संख्या को अभाज्य गुणनखंडों के गुणनफल के रूप में लिखिए।

51 = 3 \times 17

तथा

18 = 2 \times 3^{2}

432 = 2^{4} \times 3^{3}

तथा

144 = 2^{4} \times 3^{2}

ल.स. में प्रत्येक अभाज्य की उच्चतम घात ली जाती है:

2^{4} \times 3^{3} \times 17

ल.स.

= 16 \times 27 \times 17 = 432 \times 17 = 7344

इसलिए सही विकल्प (a) है।33:T77f,Equal SP, equal gain and loss When two articles are sold at the SAME price, one at a gain of

x %

and the other at a loss of

x %

, the deal is always a LOSS. Loss percentage

= \frac{x^{2}}{100}

Here x=5, so loss

= \frac{5^{2}}{100} = \frac{25}{100} = 0.25 %

Check with the actual figures: CP

= \frac{7980 \times 100}{105} = 7600

and CP

= \frac{7980 \times 100}{95} = 8400

, total 16000 against a total SP of 15960. Loss

= \frac{40}{16000} \times 100 = 0.25 %

, which confirms the shortcut. The selling price itself never enters the formula. So the correct option is (b).34:T987,समान विक्रय मूल्य पर लाभ-हानि जब दो वस्तुएँ समान विक्रय मूल्य पर बेची जाएँ, एक पर

x %

का लाभ और दूसरी पर

x %

की हानि हो, तो सौदे में सदैव हानि होती है। हानि प्रतिशत

= \frac{x^{2}}{100}

यहाँ x=5, अतः हानि

= \frac{5^{2}}{100} = \frac{25}{100} = 0.25 %

वास्तविक मानों से जाँच: क्रय मूल्य

= \frac{7980 \times 100}{105} = 7600

तथा क्रय मूल्य

= \frac{7980 \times 100}{95} = 8400

, कुल 16000, जबकि कुल विक्रय मूल्य 15960 है। हानि

= \frac{40}{16000} \times 100 = 0.25 %

, जो सूत्र की पुष्टि करता है। विक्रय मूल्य सूत्र में आता ही नहीं। इसलिए सही विकल्प (b) है।35:T432,Area of a right triangle Bring all three sides to one unit: 0.25 m =25 cm, so the sides are 7 cm, 24 cm and 25 cm. Test the sides:

7^{2} + 24^{2} = 49 + 576 = 625 = 25^{2}

The Pythagoras relation holds, so the triangle is right-angled and 25 cm is the hypotenuse - no need for Heron's formula.

The perpendicular sides are 7 cm and 24 cm, so area

= \frac{1}{2} \times 7 \times 24

Area =84 square cm So the correct option is (a).36:T5b1,समकोण त्रिभुज का क्षेत्रफल तीनों भुजाओं को एक ही इकाई में लाइए: 0.25 m =25 cm, अतः भुजाएँ 7 cm, 24 cm और 25 cm हैं। भुजाओं की जाँच कीजिए:

7^{2} + 24^{2} = 49 + 576 = 625 = 25^{2}

पाइथागोरस संबंध सत्य है, अतः त्रिभुज समकोण है और 25 cm कर्ण है - हीरोन सूत्र की आवश्यकता नहीं।

लंब भुजाएँ 7 cm और 24 cm हैं, अतः क्षेत्रफल

= \frac{1}{2} \times 7 \times 24

क्षेत्रफल =84 वर्ग cm इसलिए सही विकल्प (a) है।37:T47f,Average of remaining group Total age of the class

= 40 \times 12 = 480

years First group

= 5 \times 10 = 50

years and second group

= 5 \times 14 = 70

years Students left =40-5-5=30 Their total age =480-50-70=360 years

Average of the rest

= \frac{360}{30} = 12

years One group is 2 years below the class average and the other 2 years above it, so the two shifts cancel and the rest still average 12 years. So the correct option is (b).38:T61a,शेष समूह का औसत कक्षा की कुल आयु

= 40 \times 12 = 480

वर्ष पहला समूह

= 5 \times 10 = 50

वर्ष तथा दूसरा समूह

= 5 \times 14 = 70

वर्ष शेष विद्यार्थी =40-5-5=30 उनकी कुल आयु =480-50-70=360 वर्ष

शेष विद्यार्थियों का औसत

= \frac{360}{30} = 12

वर्ष एक समूह कक्षा के औसत से 2 वर्ष कम और दूसरा 2 वर्ष अधिक है, अतः दोनों विचलन एक-दूसरे को काट देते हैं और शेष का औसत 12 वर्ष ही रहता है। इसलिए सही विकल्प (b) है।39:T576,BODMAS with signed numbers By BODMAS, the division and the multiplication are settled before the addition and subtraction.

(- 60) \div (- 15) = 4

, because a negative divided by a negative is positive.

(- 2) \times 8 = - 16

(- 9) - (- 60) \div (- 15) + (- 2) \times 8 = (- 9) - 4 + (- 16)

=-13-16=-29 The tempting slip is to make the division negative, which gives -1 for the first two terms; keep the sign rule in mind. So the correct option is (d).3a:T710,ऋणात्मक संख्याओं में BODMAS BODMAS के अनुसार भाग और गुणा पहले किए जाते हैं, उसके बाद जोड़ और घटाव।

(- 60) \div (- 15) = 4

, क्योंकि ऋणात्मक में ऋणात्मक का भाग धनात्मक होता है।

(- 2) \times 8 = - 16

(- 9) - (- 60) \div (- 15) + (- 2) \times 8 = (- 9) - 4 + (- 16)

=-13-16=-29 सामान्य भूल यह है कि भाग का परिणाम ऋणात्मक मान लिया जाए, जिससे पहले दो पदों का मान -1 आ जाता है; चिह्न का नियम ध्यान रखिए। इसलिए सही विकल्प (d) है।3b:T50d,Profit stated in selling price Let the selling price of one chair be SP and its cost price be CP. Profit = total SP - total CP.

153 \times S P - 153 \times C P = 85 \times S P

68 \times S P = 153 \times C P

\frac{S P}{C P} = \frac{153}{68} = \frac{9}{4}

Take SP=9 and CP=4, so profit =9-4=5 per chair. Profit percentage

= \frac{5}{4} \times 100 = 125 %

Note the gain is compared with the COST price, not with the selling price - that is what rules out the neighbouring options. So the correct option is (b).3c:T6eb,विक्रय मूल्य में व्यक्त लाभ माना कि एक कुर्सी का विक्रय मूल्य SP तथा क्रय मूल्य CP है। लाभ = कुल विक्रय मूल्य - कुल क्रय मूल्य।

153 \times S P - 153 \times C P = 85 \times S P

68 \times S P = 153 \times C P

\frac{S P}{C P} = \frac{153}{68} = \frac{9}{4}

माना कि SP=9 तथा CP=4, अतः प्रति कुर्सी लाभ =9-4=5। लाभ प्रतिशत

= \frac{5}{4} \times 100 = 125 %

ध्यान दीजिए कि लाभ की तुलना क्रय मूल्य से की जाती है, विक्रय मूल्य से नहीं - यही बात निकटवर्ती विकल्पों को गलत ठहराती है। इसलिए सही विकल्प (b) है।3d:T413,Percentage of a number

2 %

of x means

\frac{2}{100} \times x

\frac{2 x}{100} = 312

x = \frac{312 \times 100}{2}

x=15600 A quick check:

2 %

\frac{1}{50}

, so x must be 50 times 312, which is 15600. So the correct option is (a).3e:T4c2,किसी संख्या का प्रतिशत x का

2 %

का अर्थ है

\frac{2}{100} \times x

।

\frac{2 x}{100} = 312

x = \frac{312 \times 100}{2}

x=15600 शीघ्र जाँच:

2 %

का अर्थ

\frac{1}{50}

है, अतः x, 312 का 50 गुना होगा, अर्थात् 15600। इसलिए सही विकल्प (a) है।1e:["$","$L28",null,{"mode":"exam","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":8841,"n":41,"subject":"Elementary Mathematics","stem":"What time (in seconds) is required for a 398 m long train to cross a 802 m long tunnel, if the train travels at a speed of 45 km/h ?","stemHi":"45 km/h की चाल से चल रही 398 m लंबी एक रेलगाड़ी को 802 m लंबी सुरंग पार करने में कितना समय (सेकंड में) लगेगा ?","context":null,"contextHi":null,"options":[{"key":"a","text":"103","textHi":null,"imageUrl":null},{"key":"b","text":"94","textHi":null,"imageUrl":null},{"key":"c","text":"93","textHi":null,"imageUrl":null},{"key":"d","text":"96","textHi":null,"imageUrl":null}],"correct":"d","sol":"Train crossing a tunnel\nTo cross a tunnel the train must cover the length of the tunnel PLUS its own length, because the tunnel is clear only when the last coach leaves the far end.\nTotal distance =398+802=1200 m\nSpeed =45 km/h

= 45 \times \frac{5}{18} = 12.5

m/s\n $\"figure\"/$ \nTime

= \frac{1200}{12.5} = 96

\nSo the required time is 96 seconds and the correct option is (d).","solHi":"रेलगाड़ी का सुरंग पार करना\nसुरंग पार करने के लिए रेलगाड़ी को सुरंग की लंबाई के साथ-साथ अपनी स्वयं की लंबाई भी तय करनी पड़ती है, क्योंकि अंतिम डिब्बा दूसरे सिरे से बाहर निकलने पर ही सुरंग पार होती है।\nकुल दूरी =398+802=1200 m\nचाल =45 km/h

= 45 \times \frac{5}{18} = 12.5

m/s\n $\"figure\"/$ \nसमय

= \frac{1200}{12.5} = 96

\nअतः अभीष्ट समय 96 सेकंड है और इसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":8842,"n":42,"subject":"Elementary Mathematics","stem":"A shopkeeper marks his jackets at 18.8% above the cost price and allows the purchaser a discount of

12.5 %

for online payment. What profit percentage does the shopkeeper make (correct to two places of decimals) ?","stemHi":"एक दुकानदार अपनी जैकेटों पर क्रय मूल्य से 18.8% अधिक मूल्य अंकित करता है और ऑनलाइन भुगतान करने पर क्रेता को

12.5 %

की छूट देता है। दुकानदार को कितने प्रतिशत का लाभ होता है (दशमलव के दो स्थानों तक सही) ?","context":null,"contextHi":null,"options":[{"key":"a","text":"5.27%","textHi":null,"imageUrl":null},{"key":"b","text":"2.58%","textHi":null,"imageUrl":null},{"key":"c","text":"

3.95 %

","textHi":null,"imageUrl":null},{"key":"d","text":"4.06%","textHi":null,"imageUrl":null}],"correct":"c","sol":"Mark-up and discount\nThe mark-up is measured on the cost price and the discount on the marked price, so take the cost price as ₹100.\nMarked price =100+18.8=118.8\nDiscount

= 12.5 %

118.8 = \frac{118.8}{8} = 14.85

\nSelling price =118.8-14.85=103.95\n $\"figure\"/$ \nProfit =103.95-100=3.95 on a cost of 100\nProfit percentage

= 3.95 %

\nSo the correct option is (c).","solHi":"अंकित मूल्य और छूट\nअंकित मूल्य क्रय मूल्य पर तथा छूट अंकित मूल्य पर लगती है, अतः माना कि क्रय मूल्य ₹100 है।\nअंकित मूल्य =100+18.8=118.8\nछूट =118.8 का

12.5 % = \frac{118.8}{8} = 14.85

\nविक्रय मूल्य =118.8-14.85=103.95\n $\"figure\"/$ \nलाभ =103.95-100=3.95 (100 के क्रय मूल्य पर)\nलाभ प्रतिशत

= 3.95 %

\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":8843,"n":43,"subject":"Elementary Mathematics","stem":"Raj has ₹1218 with him. He divided it amongst his sons Varun and Ashish and asked them to invest it at

10 %

rate of interest compounded annually. It was seen that Varun and Ashish got same amount after 13 and 14 years respectively. How much (in ₹) did Raj give to Ashish ?","stemHi":"Raj के पास ₹1218 हैं। उसने यह राशि अपने पुत्रों Varun और Ashish के बीच बाँट दी और उनसे कहा कि वे इसे

10 %

वार्षिक चक्रवृद्धि ब्याज की दर पर निवेश करें। यह देखा गया कि Varun और Ashish को क्रमशः 13 और 14 वर्षों के बाद समान राशि प्राप्त हुई। Raj ने Ashish को कितनी राशि (₹ में) दी ?","context":null,"contextHi":null,"options":[{"key":"a","text":"638","textHi":null,"imageUrl":null},{"key":"b","text":"738","textHi":null,"imageUrl":null},{"key":"c","text":"430","textHi":null,"imageUrl":null},{"key":"d","text":"580","textHi":null,"imageUrl":null}],"correct":"d","sol":"$29","solHi":"$2a","pos":2,"neg":0.25},{"id":8844,"n":44,"subject":"Elementary Mathematics","stem":"The LCM of 36, 30, 114 and 380 is:","stemHi":"36, 30, 114 और 380 का लघुत्तम समापवर्त्य (LCM) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"3440","textHi":null,"imageUrl":null},{"key":"b","text":"3420","textHi":null,"imageUrl":null},{"key":"c","text":"3475","textHi":null,"imageUrl":null},{"key":"d","text":"3456","textHi":null,"imageUrl":null}],"correct":"b","sol":"$2b","solHi":"$2c","pos":2,"neg":0.25},{"id":8845,"n":45,"subject":"Elementary Mathematics","stem":"Given that

X

is the third proportional of 20 and Y, if Y is the sum of the first three prime numbers, then the value of X is:","stemHi":"दिया गया है कि

X

, 20 और Y का तृतीय समानुपाती है, यदि Y पहली तीन अभाज्य संख्याओं का योग है, तो X का मान है:","context":null,"contextHi":null,"options":[{"key":"a","text":"6","textHi":null,"imageUrl":null},{"key":"b","text":"10","textHi":null,"imageUrl":null},{"key":"c","text":"5","textHi":null,"imageUrl":null},{"key":"d","text":"3","textHi":null,"imageUrl":null}],"correct":"c","sol":"Third proportional\nThe first three prime numbers are 2, 3 and 5 (1 is not a prime), so Y=2+3+5=10.\nIf X is the third proportional of 20 and Y, the three numbers are in continued proportion: 20:Y=Y:X.\nProduct of the means = product of the extremes:

20 \times X = Y^{2}

X = \frac{10^{2}}{20} = \frac{100}{20} = 5

\nSo the correct option is (c).","solHi":"तृतीय समानुपाती\nपहली तीन अभाज्य संख्याएँ 2, 3 और 5 हैं (1 अभाज्य नहीं है), अतः Y=2+3+5=10।\nयदि X, 20 और Y का तृतीय समानुपाती है, तो ये तीनों संख्याएँ सतत समानुपात में हैं: 20:Y=Y:X।\nमध्य पदों का गुणनफल = अंत्य पदों का गुणनफल:

20 \times X = Y^{2}

X = \frac{10^{2}}{20} = \frac{100}{20} = 5

\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":8846,"n":46,"subject":"Elementary Mathematics","stem":"A, B and C can do a piece of work in 22 days, 24 days and 33 days, respectively. In how many days will the work be finished if, A works on the

1^{st}

day, C works on the

2^{nd}

day, B works on the

3^{rd}

day, A works on the

4^{th}

day and so on ?","stemHi":"A, B और C किसी कार्य को क्रमशः 22 दिन, 24 दिन और 33 दिन में पूरा कर सकते हैं। यदि A

1^{st}

दिन कार्य करता है, C

2^{nd}

दिन कार्य करता है, B

3^{rd}

दिन कार्य करता है, A

4^{th}

दिन कार्य करता है और इसी क्रम में आगे भी कार्य होता रहे, तो कार्य कितने दिनों में समाप्त होगा ?","context":null,"contextHi":null,"options":[{"key":"a","text":"24","textHi":null,"imageUrl":null},{"key":"b","text":"

28 \frac{1}{3}

","textHi":null,"imageUrl":null},{"key":"c","text":"

25 \frac{1}{2}

","textHi":null,"imageUrl":null},{"key":"d","text":"

22 \frac{2}{3}

","textHi":null,"imageUrl":null}],"correct":"c","sol":"$2d","solHi":"$2e","pos":2,"neg":0.25},{"id":8847,"n":47,"subject":"Elementary Mathematics","stem":"The fourth proportional to 4, a and

16 a

is 81 . Find the value of

a^{2}

.","stemHi":"4, a और

16 a

का चतुर्थ समानुपाती 81 है।

a^{2}

का मान ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"20.25","textHi":null,"imageUrl":null},{"key":"b","text":"16.5","textHi":null,"imageUrl":null},{"key":"c","text":"22.5","textHi":null,"imageUrl":null},{"key":"d","text":"24.75","textHi":null,"imageUrl":null}],"correct":"a","sol":"Fourth proportional\nIf d is the fourth proportional to a, b and c, then a:b=c:d.\nHere 4:a=16a:81\nProduct of the extremes = product of the means:

4 \times 81 = a \times 16 a

324 = 16 a^{2}

a^{2} = \frac{324}{16} = 20.25

\nSo the correct option is (a).","solHi":"चतुर्थ समानुपाती\nयदि d, संख्याओं a, b और c का चतुर्थ समानुपाती है, तो a:b=c:d होता है।\nयहाँ 4:a=16a:81\nअंत्य पदों का गुणनफल = मध्य पदों का गुणनफल:

4 \times 81 = a \times 16 a

324 = 16 a^{2}

a^{2} = \frac{324}{16} = 20.25

\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":8848,"n":48,"subject":"Elementary Mathematics","stem":"Aditya appeared in a competitive exam in which the final grades are determined by three different exams of 100 marks having weights

20 %, 35 %

and 45%, respectively. If Aditya scored 80, 70 and 60 marks in these exams, respectively, then what is the weighted average score of Aditya ?","stemHi":"Aditya एक प्रतियोगी परीक्षा में सम्मिलित हुआ, जिसमें अंतिम ग्रेड 100-100 अंकों की तीन अलग-अलग परीक्षाओं से निर्धारित होते हैं, जिनके भार क्रमशः

20 %, 35 %

और 45% हैं। यदि Aditya ने इन परीक्षाओं में क्रमशः 80, 70 और 60 अंक प्राप्त किए, तो Aditya का भारित औसत स्कोर क्या है ?","context":null,"contextHi":null,"options":[{"key":"a","text":"67","textHi":null,"imageUrl":null},{"key":"b","text":"66.5","textHi":null,"imageUrl":null},{"key":"c","text":"67.5","textHi":null,"imageUrl":null},{"key":"d","text":"66","textHi":null,"imageUrl":null}],"correct":"c","sol":"Weighted average\nA weighted average multiplies every score by its own weight and divides by the total weight - a plain average of 80, 70 and 60 would be wrong here.\nTotal weight =20+35+45=100\n $\"figure\"/$ \nWeighted total

= 80 \times 20 + 70 \times 35 + 60 \times 45

\n=1600+2450+2700=6750\nWeighted average

= \frac{6750}{100} = 67.5

\nSo the correct option is (c).","solHi":"भारित औसत\nभारित औसत में प्रत्येक अंक को उसके भार से गुणा करके कुल भार से भाग दिया जाता है - यहाँ 80, 70 और 60 का साधारण औसत लेना गलत होगा।\nकुल भार =20+35+45=100\n $\"figure\"/$ \nभारित योग

= 80 \times 20 + 70 \times 35 + 60 \times 45

\n=1600+2450+2700=6750\nभारित औसत

= \frac{6750}{100} = 67.5

\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":8849,"n":49,"subject":"Elementary Mathematics","stem":"If at the same rate of interest, in 2 years, the simple interest is ₹40 and compound interest is ₹50, then what is the principal (in ₹) ?","stemHi":"यदि समान ब्याज दर पर 2 वर्षों में साधारण ब्याज ₹40 और चक्रवृद्धि ब्याज ₹50 है, तो मूलधन (₹ में) क्या है ?","context":null,"contextHi":null,"options":[{"key":"a","text":"40","textHi":null,"imageUrl":null},{"key":"b","text":"35","textHi":null,"imageUrl":null},{"key":"c","text":"33","textHi":null,"imageUrl":null},{"key":"d","text":"44","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2f","solHi":"$30","pos":2,"neg":0.25},{"id":8850,"n":50,"subject":"Elementary Mathematics","stem":"Evaluate:

16 + 12 \div 3 - 2 \times 3

","stemHi":"मान ज्ञात कीजिए:

16 + 12 \div 3 - 2 \times 3

","context":null,"contextHi":null,"options":[{"key":"a","text":"17","textHi":null,"imageUrl":null},{"key":"b","text":"13","textHi":null,"imageUrl":null},{"key":"c","text":"16","textHi":null,"imageUrl":null},{"key":"d","text":"14","textHi":null,"imageUrl":null}],"correct":"d","sol":"BODMAS simplification\nBy BODMAS, division and multiplication are done before addition and subtraction.\n

12 \div 3 = 4

and

2 \times 3 = 6

16 + 12 \div 3 - 2 \times 3 = 16 + 4 - 6

\n=20-6=14\nSo the correct option is (d).","solHi":"BODMAS द्वारा सरलीकरण\nBODMAS के अनुसार, भाग और गुणा, जोड़ और घटाव से पहले किए जाते हैं।\n

12 \div 3 = 4

तथा

2 \times 3 = 6

16 + 12 \div 3 - 2 \times 3 = 16 + 4 - 6

\n=20-6=14\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":8851,"n":51,"subject":"Elementary Mathematics","stem":"The LCM of 51, 18, 432 and 144 is:","stemHi":"51, 18, 432 और 144 का लघुत्तम समापवर्त्य (LCM) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"7344","textHi":null,"imageUrl":null},{"key":"b","text":"7276","textHi":null,"imageUrl":null},{"key":"c","text":"7320","textHi":null,"imageUrl":null},{"key":"d","text":"7294","textHi":null,"imageUrl":null}],"correct":"a","sol":"$31","solHi":"$32","pos":2,"neg":0.25},{"id":8852,"n":52,"subject":"Elementary Mathematics","stem":"Two televisions are sold for ₹7,980 each, gaining 5% from one and losing 5% from the other. Find the gain or loss percentage in the whole transaction.","stemHi":"दो टेलीविजन ₹7,980 प्रत्येक की दर से बेचे जाते हैं, जिनमें से एक पर 5% का लाभ और दूसरे पर 5% की हानि होती है। पूरे लेन-देन में लाभ या हानि प्रतिशत ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"

0.5 %

loss","textHi":"

0.5 %

हानि","imageUrl":null},{"key":"b","text":"

0.25 %

loss","textHi":"

0.25 %

हानि","imageUrl":null},{"key":"c","text":"

0.25 %

gain","textHi":"

0.25 %

लाभ","imageUrl":null},{"key":"d","text":"0.5% gain","textHi":"0.5% लाभ","imageUrl":null}],"correct":"b","sol":"$33","solHi":"$34","pos":2,"neg":0.25},{"id":8853,"n":53,"subject":"Elementary Mathematics","stem":"Find the area (in

{cm}^{2}

) of a triangle whose length of each side is

7 cm, 24 cm

and 0.25 m.","stemHi":"उस त्रिभुज का क्षेत्रफल (

{cm}^{2}

में) ज्ञात कीजिए जिसकी भुजाओं की लंबाई

7 cm, 24 cm

और 0.25 m है।","context":null,"contextHi":null,"options":[{"key":"a","text":"84","textHi":null,"imageUrl":null},{"key":"b","text":"72","textHi":null,"imageUrl":null},{"key":"c","text":"42","textHi":null,"imageUrl":null},{"key":"d","text":"56","textHi":null,"imageUrl":null}],"correct":"a","sol":"$35","solHi":"$36","pos":2,"neg":0.25},{"id":8854,"n":54,"subject":"Elementary Mathematics","stem":"The average age of 40 students in a class is 12 years. The average age of group of 5 of students is 10 years and that of another group of 5 of them is 14 years. The average age of the remaining students is:","stemHi":"एक कक्षा के 40 विद्यार्थियों की औसत आयु 12 वर्ष है। उनमें से 5 विद्यार्थियों के एक समूह की औसत आयु 10 वर्ष है तथा अन्य 5 विद्यार्थियों के एक दूसरे समूह की औसत आयु 14 वर्ष है। शेष विद्यार्थियों की औसत आयु है:","context":null,"contextHi":null,"options":[{"key":"a","text":"13 years","textHi":null,"imageUrl":null},{"key":"b","text":"12 years","textHi":null,"imageUrl":null},{"key":"c","text":"10 years","textHi":null,"imageUrl":null},{"key":"d","text":"11 years","textHi":null,"imageUrl":null}],"correct":"b","sol":"$37","solHi":"$38","pos":2,"neg":0.25},{"id":8855,"n":55,"subject":"Elementary Mathematics","stem":"The price (per litre) of petrol increases by 90%. By what percent should its consumption be reduced such that the expenditure on it increases by 33% only ?","stemHi":"पेट्रोल के मूल्य (प्रति लीटर) में 90% की वृद्धि होती है। इसकी खपत में कितने प्रतिशत की कमी की जानी चाहिए, ताकि इस पर होने वाले व्यय में केवल 33% की ही वृद्धि हो ?","context":null,"contextHi":null,"options":[{"key":"a","text":"30%","textHi":null,"imageUrl":null},{"key":"b","text":"64%","textHi":null,"imageUrl":null},{"key":"c","text":"70%","textHi":null,"imageUrl":null},{"key":"d","text":"36%","textHi":null,"imageUrl":null}],"correct":"a","sol":"Price rise and consumption cut\nExpenditure = price × consumption, so take both the price and the expenditure as 100 to start with.\nNew price =100+90=190 and the new expenditure =100+33=133\nNew consumption

= \frac{133}{190} \times 100 = 70

\n $\"figure\"/$ \nFall in consumption =100-70=30\nReduction

= \frac{30}{100} \times 100 = 30 %

\nSo the correct option is (a).","solHi":"मूल्य वृद्धि और खपत में कमी\nव्यय = मूल्य × खपत, अतः प्रारंभ में मूल्य और व्यय दोनों को 100 मानिए।\nनया मूल्य =100+90=190 तथा नया व्यय =100+33=133\nनई खपत

= \frac{133}{190} \times 100 = 70

\n $\"figure\"/$ \nखपत में कमी =100-70=30\nकमी

= \frac{30}{100} \times 100 = 30 %

\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":8856,"n":56,"subject":"Elementary Mathematics","stem":"Chetan invests a sum of ₹5400 and Vipul invests a sum of ₹10200 at the same rate of simple interest per annum. If, at the end of 3 years, Vipul gets ₹720 more interest than Chetan, then find the rate of interest per annum (in percentage).","stemHi":"Chetan ₹5400 की राशि तथा Vipul ₹10200 की राशि समान वार्षिक साधारण ब्याज दर पर निवेश करते हैं। यदि 3 वर्षों के अंत में Vipul को Chetan से ₹720 अधिक ब्याज मिलता है, तो वार्षिक ब्याज दर (प्रतिशत में) ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"4","textHi":null,"imageUrl":null},{"key":"b","text":"3","textHi":null,"imageUrl":null},{"key":"c","text":"5","textHi":null,"imageUrl":null},{"key":"d","text":"7","textHi":null,"imageUrl":null}],"correct":"c","sol":"Simple interest rate\nBoth sums run at the same rate for the same 3 years, so the extra interest comes only from the extra principal.\nExtra principal =10200-5400=4800\n

\frac{4800 \times R \times 3}{100} = 720

\n144R=720\n

R = \frac{720}{144} = 5

\nSo the rate is

5 %

per annum and the correct option is (c).","solHi":"साधारण ब्याज की दर\nदोनों राशियाँ समान दर पर समान 3 वर्षों के लिए लगी हैं, अतः अतिरिक्त ब्याज केवल अतिरिक्त मूलधन से आता है।\nअतिरिक्त मूलधन =10200-5400=4800\n

\frac{4800 \times R \times 3}{100} = 720

\n144R=720\n

R = \frac{720}{144} = 5

\nअतः ब्याज दर

5 %

वार्षिक है और इसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":8857,"n":57,"subject":"Elementary Mathematics","stem":"Evaluate:

(- 9) - (- 60) \div (- 15) + (- 2) \times 8

","stemHi":"मान ज्ञात कीजिए:

(- 9) - (- 60) \div (- 15) + (- 2) \times 8

","context":null,"contextHi":null,"options":[{"key":"a","text":"-28","textHi":null,"imageUrl":null},{"key":"b","text":"-31","textHi":null,"imageUrl":null},{"key":"c","text":"-32","textHi":null,"imageUrl":null},{"key":"d","text":"-29","textHi":null,"imageUrl":null}],"correct":"d","sol":"$39","solHi":"$3a","pos":2,"neg":0.25},{"id":8858,"n":58,"subject":"Elementary Mathematics","stem":"Sachin sold 153 chairs and had a gain equal to the selling price of 85 chairs. What is his profit percentage ?","stemHi":"Sachin ने 153 कुर्सियाँ बेचीं और उसे 85 कुर्सियों के विक्रय मूल्य के बराबर लाभ हुआ। उसका लाभ प्रतिशत क्या है ?","context":null,"contextHi":null,"options":[{"key":"a","text":"135%","textHi":null,"imageUrl":null},{"key":"b","text":"125%","textHi":null,"imageUrl":null},{"key":"c","text":"

120 %

","textHi":null,"imageUrl":null},{"key":"d","text":"130%","textHi":null,"imageUrl":null}],"correct":"b","sol":"$3b","solHi":"$3c","pos":2,"neg":0.25},{"id":8859,"n":59,"subject":"Elementary Mathematics","stem":"If

2 %

x = 312

, then

x

is equal to:","stemHi":"यदि

2 %

x = 312

है, तो

x

का मान होगा:","context":null,"contextHi":null,"options":[{"key":"a","text":"15600","textHi":null,"imageUrl":null},{"key":"b","text":"31200","textHi":null,"imageUrl":null},{"key":"c","text":"31300","textHi":null,"imageUrl":null},{"key":"d","text":"15700","textHi":null,"imageUrl":null}],"correct":"a","sol":"$3d","solHi":"$3e","pos":2,"neg":0.25},{"id":8860,"n":60,"subject":"Elementary Mathematics","stem":"Two trains, 200 m and 250 m long, are moving in the same direction at speeds of

80 km / hr

and

60 km / hr

, respectively. How long (in seconds) will it take for the faster train to completely pass the slower one ?","stemHi":"दो रेलगाड़ियाँ, जिनकी लंबाई 200 m और 250 m है, एक ही दिशा में क्रमशः

80 km / hr

और

60 km / hr

की चाल से चल रही हैं। तेज़ चलने वाली रेलगाड़ी को धीमी रेलगाड़ी को पूरी तरह पार करने में कितना समय (सेकंड में) लगेगा ?","context":null,"contextHi":null,"options":[{"key":"a","text":"81","textHi":null,"imageUrl":null},{"key":"b","text":"77","textHi":null,"imageUrl":null},{"key":"c","text":"79","textHi":null,"imageUrl":null},{"key":"d","text":"75","textHi":null,"imageUrl":null}],"correct":"a","sol":"Trains in the same direction\nMoving in the SAME direction, the faster train gains on the slower one at the DIFFERENCE of their speeds.\nRelative speed =80-60=20 km/h

= 20 \times \frac{5}{18} = \frac{50}{9}

m/s\nTo pass completely, the faster train must cover both lengths: 200+250=450 m\n $\"figure\"/$ \nTime

= 450 \div \frac{50}{9} = 450 \times \frac{9}{50}

\nTime =81 seconds\nSo the correct option is (a).","solHi":"एक ही दिशा में चलती रेलगाड़ियाँ\nएक ही दिशा में चलने पर तेज़ रेलगाड़ी धीमी रेलगाड़ी पर चालों के अंतर की दर से बढ़त बनाती है।\nसापेक्ष चाल =80-60=20 km/h

= 20 \times \frac{5}{18} = \frac{50}{9}

m/s\nपूरी तरह पार करने के लिए तेज़ रेलगाड़ी को दोनों लंबाइयाँ तय करनी होंगी: 200+250=450 m\n $\"figure\"/$ \nसमय

= 450 \div \frac{50}{9} = 450 \times \frac{9}{50}

\nसमय =81 सेकंड\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25}],"test":{"slug":"ssc-gd-constable--18-feb-2025-shift-2-maths","title":"SSC GD Constable 18 February 2025 Shift-2 — Elementary Mathematics Sectional Test","examName":"SSC GD","paperLabel":"18 February 2025 · Shift 2","sectionSubject":"Elementary Mathematics","durationMinutes":15,"format":"sectional_test"}}]