26:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 27:T40b,Circular track, opposite directions Starting together and moving in opposite directions, they meet when the two of them together have covered one full lap, i.e. 1500 m.

Opposite directions, so relative speed =18+22=40 km/hr. 40 km/hr

= 40 \times \frac{5}{18} = \frac{100}{9}

m/s. Time to meet

= \frac{1500}{\frac{100}{9}} = 1500 \times \frac{9}{100} = 135

s. So the correct option is (d).28:T4e3,Percentage, literacy Females =372000-168000=204000. Total literates

= 20 %

372000 = \frac{20}{100} \times 372000 = 74400

. Literate males

= 20 %

168000 = \frac{20}{100} \times 168000 = 33600

. Literate females =74400-33600=40800.

Required percentage

= \frac{40800}{204000} \times 100 = 20 %

. So the correct option is (a).29:T752,Compound interest, equal amounts At

5 %

compounded annually, Amount

= P {(1 + \frac{5}{100})}^{n} = P {(\frac{21}{20})}^{n}

. Let Ashish get A and Arun get B. Their amounts are equal after 11 and 12 years:

A {(\frac{21}{20})}^{11} = B {(\frac{21}{20})}^{12}

\frac{A}{B} = \frac{21}{20}

, so A:B=21:20 - the son who invests longer gets less money. 21+20=41 units =₹1230, so 1 unit

= \frac{1230}{41} = ₹ 30

. Arun's share

= 20 \times 30 = ₹ 600

. So the correct option is (a).2a:T8db,चक्रवृद्धि ब्याज, समान राशि वार्षिक चक्रवृद्धि पर

5 %

की दर से, मिश्रधन

= P {(1 + \frac{5}{100})}^{n} = P {(\frac{21}{20})}^{n}

। माना कि आशीष को A और अरुण को B मिलता है। 11 और 12 वर्ष बाद उनकी राशियाँ बराबर हैं:

A {(\frac{21}{20})}^{11} = B {(\frac{21}{20})}^{12}

\frac{A}{B} = \frac{21}{20}

, अतः A:B=21:20 - जो अधिक समय तक निवेश करता है उसे कम मूलधन मिलता है। 21+20=41 इकाई =₹1230, अतः 1 इकाई

= \frac{1230}{41} = ₹ 30

। अरुण का भाग

= 20 \times 30 = ₹ 600

। इसलिए सही विकल्प (a) है।2b:T53a,Volume of a cylinder The question gives the diameter, so halve it first: radius

= \frac{6}{2} = 3

cm.

Volume of a cylinder

= π r^{2} h

= \frac{22}{7} \times 3^{2} \times 14

= \frac{22}{7} \times 9 \times 14 = 22 \times 9 \times 2

= 396 {cm}^{3}

So the correct option is (a).2c:T5d7,बेलन का आयतन प्रश्न में व्यास दिया है, अतः पहले उसे आधा कीजिए: त्रिज्या

= \frac{6}{2} = 3

सेमी।

बेलन का आयतन

= π r^{2} h

= \frac{22}{7} \times 3^{2} \times 14

= \frac{22}{7} \times 9 \times 14 = 22 \times 9 \times 2

= 396 {cm}^{3}

इसलिए सही विकल्प (a) है।2d:T882,Time and work, cyclic pattern Take the total work as

LCM (15, 30, 40) = 120

units. One day's work:

A = \frac{120}{15} = 8

B = \frac{120}{30} = 4

C = \frac{120}{40} = 3

units.

One cycle of 3 days =8+12+11=31 units. Three cycles =9 days

= 3 \times 31 = 93

units. Day 10 (A alone)

\to 93 + 8 = 101

; day 11 (A and B)

\to 101 + 12 = 113

units. Remaining =120-113=7 units, and day 12 belongs to A and C, who do 11 units a day. Extra time

= \frac{7}{11}

day. Total time

= 11 + \frac{7}{11} = 11 \frac{7}{11}

days. So the correct option is (a).2e:Ta1c,समय और कार्य, चक्रीय क्रम कुल कार्य

= LCM (15, 30, 40) = 120

इकाई मानिए। एक दिन का कार्य:

A = \frac{120}{15} = 8

B = \frac{120}{30} = 4

C = \frac{120}{40} = 3

इकाई।

3 दिन के एक चक्र में कार्य =8+12+11=31 इकाई। तीन चक्र =9 दिन

= 3 \times 31 = 93

इकाई। 10वें दिन (केवल A)

\to 93 + 8 = 101

; 11वें दिन (A और B)

\to 101 + 12 = 113

इकाई। शेष कार्य =120-113=7 इकाई, और 12वाँ दिन A तथा C का है, जो एक दिन में 11 इकाई करते हैं। अतिरिक्त समय

= \frac{7}{11}

दिन। कुल समय

= 11 + \frac{7}{11} = 11 \frac{7}{11}

दिन। इसलिए सही विकल्प (a) है।2f:T482,Successive discounts Successive discounts are applied one after the other, so the multipliers multiply. SP

= 52300 \times \frac{100 - 20}{100} \times \frac{100 - 4}{100}

= 52300 \times \frac{80}{100} \times \frac{96}{100}

= 41840 \times \frac{96}{100} = 40166.4

Rounded to the nearest rupee, SP =₹40,166. Adding the discounts to get

24 %

would give ₹39,748, which is why that shortcut fails. So the correct option is (c).30:T5ce,क्रमिक छूट क्रमिक छूट एक के बाद एक लगती है, अतः उनके गुणक आपस में गुणा होते हैं। विक्रय मूल्य

= 52300 \times \frac{100 - 20}{100} \times \frac{100 - 4}{100}

= 52300 \times \frac{80}{100} \times \frac{96}{100}

= 41840 \times \frac{96}{100} = 40166.4

निकटतम रुपये तक पूर्णांकित करने पर विक्रय मूल्य =₹40,166। छूटों को जोड़कर

24 %

लेने पर ₹39,748 मिलता, इसीलिए वह शॉर्टकट गलत है। इसलिए सही विकल्प (c) है।31:T4e2,Direct proportion

F \propto m

means

\frac{F}{m}

stays constant, so

\frac{F_{1}}{m_{1}} = \frac{F_{2}}{m_{2}}

\frac{10}{2} = \frac{F_{2}}{5}

F_{2} = 5 \times 5 = 25

So the required force is 25 N, i.e. option (a).32:T555,सीधा अनुपात

F \propto m

का अर्थ है कि

\frac{F}{m}

अचर रहता है, अतः

\frac{F_{1}}{m_{1}} = \frac{F_{2}}{m_{2}}

।

\frac{10}{2} = \frac{F_{2}}{5}

F_{2} = 5 \times 5 = 25

अतः अभीष्ट बल 25 N है, अर्थात् विकल्प (a)।33:T4a9,Trains crossing, same direction To cross completely, the faster train must cover the sum of the two lengths. Distance =450+350=800 m.

Same direction, so relative speed =110-80=30 km/h. 30 km/h

= 30 \times \frac{5}{18} = \frac{25}{3}

m/s. Time

= \frac{800}{\frac{25}{3}} = 800 \times \frac{3}{25} = 96

s. The answer is asked in minutes:

\frac{96}{60} = 1.6

minutes. So the correct option is (c).34:T608,रेलगाड़ियाँ, समान दिशा पूरी तरह पार करने के लिए तेज़ रेलगाड़ी को दोनों लंबाइयों का योग तय करना होगा। दूरी =450+350=800 मी।

समान दिशा होने से सापेक्ष चाल =110-80=30 किमी/घंटा। 30 किमी/घंटा

= 30 \times \frac{5}{18} = \frac{25}{3}

मी/से। समय

= \frac{800}{\frac{25}{3}} = 800 \times \frac{3}{25} = 96

से। उत्तर मिनट में पूछा गया है:

\frac{96}{60} = 1.6

मिनट। इसलिए सही विकल्प (c) है।35:T733,Compound interest, equal amounts At

4 %

compounded annually, Amount

= P {(1 + \frac{4}{100})}^{n} = P {(\frac{26}{25})}^{n}

. Let Nitin get N and Pravin get P; their amounts are equal after 12 and 13 years:

N {(\frac{26}{25})}^{12} = P {(\frac{26}{25})}^{13}

\frac{N}{P} = \frac{26}{25}

, so Nitin : Pravin =26:25. 26+25=51 units =₹1632, so 1 unit

= \frac{1632}{51} = ₹ 32

. Nitin's share

= 26 \times 32 = ₹ 832

. So the correct option is (b).36:T884,चक्रवृद्धि ब्याज, समान राशि वार्षिक चक्रवृद्धि पर

4 %

की दर से, मिश्रधन

= P {(1 + \frac{4}{100})}^{n} = P {(\frac{26}{25})}^{n}

। माना कि नितिन को N और प्रवीण को P मिलता है; 12 और 13 वर्ष बाद उनकी राशियाँ बराबर हैं:

N {(\frac{26}{25})}^{12} = P {(\frac{26}{25})}^{13}

\frac{N}{P} = \frac{26}{25}

, अतः नितिन : प्रवीण =26:25। 26+25=51 इकाई =₹1632, अतः 1 इकाई

= \frac{1632}{51} = ₹ 32

। नितिन का भाग

= 26 \times 32 = ₹ 832

। इसलिए सही विकल्प (b) है।1c:["$","$L26",null,{"mode":"practice","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":13441,"n":41,"subject":"Elementary Mathematics","stem":"A car runs for one hour with a speed 60 km per hour, for 2 hours with a speed 70 km per hour and for 5 hours with a speed 50 km per hour. What is the average speed of the car in km per hour?","stemHi":"एक कार 60 किमी प्रति घंटा की चाल से एक घंटे तक, 70 किमी प्रति घंटा की चाल से 2 घंटे तक और 50 किमी प्रति घंटा की चाल से 5 घंटे तक चलती है। कार की औसत चाल (किमी प्रति घंटा में) कितनी है?","context":null,"contextHi":null,"options":[{"key":"a","text":"56.25","textHi":null,"imageUrl":null},{"key":"b","text":"53.33","textHi":null,"imageUrl":null},{"key":"c","text":"55.62","textHi":null,"imageUrl":null},{"key":"d","text":"52.65","textHi":null,"imageUrl":null}],"correct":"a","sol":"Average speed\nAverage speed is total distance divided by total time, never the average of the speeds.\nDistance of each leg = speed

\times

time.\n $\"figure\"/$ \nTotal distance =60+140+250=450 km.\nTotal time =1+2+5=8 hours.\nAverage speed

= \frac{450}{8} = 56.25

km/h.\nSo the correct option is (a).","solHi":"औसत चाल\nऔसत चाल = कुल दूरी ÷ कुल समय होती है, यह चालों का औसत कभी नहीं होती।\nप्रत्येक चरण की दूरी = चाल

\times

समय।\n $\"figure\"/$ \nकुल दूरी =60+140+250=450 किमी।\nकुल समय =1+2+5=8 घंटे।\nऔसत चाल

= \frac{450}{8} = 56.25

किमी/घंटा।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":13442,"n":42,"subject":"Elementary Mathematics","stem":"Find the value of\n

((90 \div 5) \times (\frac{78}{6} + \frac{12}{1} \times (8 - 7)))

","stemHi":"निम्नलिखित का मान ज्ञात कीजिए।\n

((90 \div 5) \times (\frac{78}{6} + \frac{12}{1} \times (8 - 7)))

","context":null,"contextHi":null,"options":[{"key":"a","text":"450","textHi":null,"imageUrl":null},{"key":"b","text":"462","textHi":null,"imageUrl":null},{"key":"c","text":"463","textHi":null,"imageUrl":null},{"key":"d","text":"458","textHi":null,"imageUrl":null}],"correct":"a","sol":"BODMAS simplification\nWork outwards from the innermost bracket (BODMAS).\nInside the curly bracket:

\frac{78}{6} + \frac{12}{1} \times (8 - 7) = 13 + 12 \times 1 = 13 + 12 = 25

.\nInside the round bracket:

90 \div 5 = 18

.\nNow multiply:

18 \times 25 = 450

.\nSo the correct option is (a).","solHi":"बोडमास सरलीकरण\nसबसे भीतरी कोष्ठक से बाहर की ओर हल कीजिए (बोडमास)।\nमझले कोष्ठक में:

\frac{78}{6} + \frac{12}{1} \times (8 - 7) = 13 + 12 \times 1 = 13 + 12 = 25

।\nगोल कोष्ठक में:

90 \div 5 = 18

।\nअब गुणा कीजिए:

18 \times 25 = 450

।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":13443,"n":43,"subject":"Elementary Mathematics","stem":"When the numbers 8651, 8018 and 7807 were divided by the greatest number x , then the remainder in each case was the same. The value of

x

is:","stemHi":"जब संख्याओं 8651, 8018 और 7807 को महत्तम संख्या x से विभाजित किया गया, तो प्रत्येक स्थिति में शेषफल समान था।

x

का मान है:","context":null,"contextHi":null,"options":[{"key":"a","text":"119","textHi":null,"imageUrl":null},{"key":"b","text":"132","textHi":null,"imageUrl":null},{"key":"c","text":"207","textHi":null,"imageUrl":null},{"key":"d","text":"211","textHi":null,"imageUrl":null}],"correct":"d","sol":"HCF, equal remainders\nIf three numbers leave the same remainder when divided by x, then x divides every difference of those numbers exactly.\nSo the greatest such x is the HCF of the differences.\n $\"figure\"/$ \n

633 = 3 \times 211

and

844 = 4 \times 211

, so

HCF (633, 211, 844) = 211

.\nHence x=211.\nSo the correct option is (d).","solHi":"म.स., समान शेषफल\nयदि तीन संख्याओं को x से भाग देने पर शेषफल समान रहता है, तो x उन संख्याओं के प्रत्येक अंतर को पूरा-पूरा विभाजित करता है।\nअतः ऐसा महत्तम x इन अंतरों का म.स. होगा।\n $\"figure\"/$ \n

633 = 3 \times 211

तथा

844 = 4 \times 211

, अतः

HCF (633, 211, 844) = 211

।\nअतः x=211।\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":13444,"n":44,"subject":"Elementary Mathematics","stem":"The ratio between the original price of a movie ticket and increased price of the movie ticket is 10 : 13. What is the increase in the revenue of the cinema hall, if the original price of the movie ticket was ₹250 and total 3600 tickets were sold as per the maximum capacity of the cinema hall that is 3600 persons?","stemHi":"एक मूवी टिकट की मूल कीमत और बढ़ी हुई कीमत के बीच का अनुपात 10 : 13 है। सिनेमा हॉल के राजस्व में कितनी वृद्धि हुई, यदि मूवी टिकट की मूल कीमत ₹250 थी और सिनेमा हॉल की अधिकतम क्षमता 3600 व्यक्ति के अनुसार कुल 3600 टिकट बेचे गए?","context":null,"contextHi":null,"options":[{"key":"a","text":"₹2,70,000","textHi":null,"imageUrl":null},{"key":"b","text":"₹1,28,000","textHi":null,"imageUrl":null},{"key":"c","text":"₹82,000","textHi":null,"imageUrl":null},{"key":"d","text":"₹1,98,000","textHi":null,"imageUrl":null}],"correct":"a","sol":"Ratio and revenue\nOriginal : increased price =10:13.\n10 units =₹250, so 1 unit

= \frac{250}{10} = ₹ 25

.\nIncreased price

= 13 \times 25 = ₹ 325

.\nIncrease per ticket =325-250=₹75.\nAll 3600 seats were sold, so increase in revenue

= 75 \times 3600 = ₹ 2, 70, 000

.\nSo the correct option is (a).","solHi":"अनुपात और राजस्व\nमूल कीमत : बढ़ी हुई कीमत =10:13।\n10 इकाई =₹250, अतः 1 इकाई

= \frac{250}{10} = ₹ 25

।\nबढ़ी हुई कीमत

= 13 \times 25 = ₹ 325

।\nप्रति टिकट वृद्धि =325-250=₹75।\nसभी 3600 सीटें बिकीं, अतः राजस्व में वृद्धि

= 75 \times 3600 = ₹ 2, 70, 000

।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":13445,"n":45,"subject":"Elementary Mathematics","stem":"When the numbers 7807, 8022 and 8667 were divided by the greatest number x , then the remainder in each case was the same. The sum of the digits of x is:","stemHi":"जब संख्याओं 7807, 8022 और 8667 को महत्तम संख्या x से विभाजित किया गया, तो प्रत्येक स्थिति में शेषफल समान था। x के अंकों का योग है:","context":null,"contextHi":null,"options":[{"key":"a","text":"8","textHi":null,"imageUrl":null},{"key":"b","text":"9","textHi":null,"imageUrl":null},{"key":"c","text":"6","textHi":null,"imageUrl":null},{"key":"d","text":"7","textHi":null,"imageUrl":null}],"correct":"a","sol":"HCF, equal remainders\nEqual remainders mean x divides each pairwise difference exactly, so the greatest x is the HCF of the differences.\n $\"figure\"/$ \n

645 = 3 \times 215

and

860 = 4 \times 215

, so

HCF (215, 645, 860) = 215

.\nHence x=215.\nSum of the digits =2+1+5=8.\nSo the correct option is (a).","solHi":"म.स., समान शेषफल\nशेषफल समान होने का अर्थ है कि x प्रत्येक अंतर को पूरा-पूरा विभाजित करता है, अतः महत्तम x इन अंतरों का म.स. है।\n $\"figure\"/$ \n

645 = 3 \times 215

तथा

860 = 4 \times 215

, अतः

HCF (215, 645, 860) = 215

।\nअतः x=215।\nअंकों का योग =2+1+5=8।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":13446,"n":46,"subject":"Elementary Mathematics","stem":"Two cyclists, M and N , start from the same point on a 1500 m circular track, cycling in opposite directions. M cycles at 18 km/hr and N at 22 km/hr. How long (in seconds) will it take for them to meet ?","stemHi":"दो साइकिल चालक, M और N, 1500 मी के वृत्ताकार पथ पर एक ही बिंदु से विपरीत दिशाओं में साइकिल चलाना आरंभ करते हैं। M की चाल 18 किमी/घंटा और N की चाल 22 किमी/घंटा है। उन्हें मिलने में कितना समय (सेकंड में) लगेगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"132","textHi":null,"imageUrl":null},{"key":"b","text":"127","textHi":null,"imageUrl":null},{"key":"c","text":"130","textHi":null,"imageUrl":null},{"key":"d","text":"135","textHi":null,"imageUrl":null}],"correct":"d","sol":"$27","solHi":"वृत्ताकार पथ, विपरीत दिशा\nएक ही बिंदु से विपरीत दिशाओं में चलने पर वे तब मिलते हैं जब दोनों मिलकर एक पूरा चक्कर, अर्थात् 1500 मी, तय कर लेते हैं।\n $\"figure\"/$ \nविपरीत दिशाएँ होने से सापेक्ष चाल =18+22=40 किमी/घंटा।\n40 किमी/घंटा

= 40 \times \frac{5}{18} = \frac{100}{9}

मी/से।\nमिलने में लगा समय

= \frac{1500}{\frac{100}{9}} = 1500 \times \frac{9}{100} = 135

से।\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":13447,"n":47,"subject":"Elementary Mathematics","stem":"Find the value of\n

((25 \times 13) \times (2 \div 2 \times \frac{(16 - 13)}{3}))

","stemHi":"निम्नलिखित का मान ज्ञात कीजिए।\n

((25 \times 13) \times (2 \div 2 \times \frac{(16 - 13)}{3}))

","context":null,"contextHi":null,"options":[{"key":"a","text":"344","textHi":null,"imageUrl":null},{"key":"b","text":"313","textHi":null,"imageUrl":null},{"key":"c","text":"325","textHi":null,"imageUrl":null},{"key":"d","text":"312","textHi":null,"imageUrl":null}],"correct":"c","sol":"BODMAS simplification\nSimplify the innermost bracket first (BODMAS).\n16-13=3, so

\frac{(16 - 13)}{3} = \frac{3}{3} = 1

.\nCurly bracket

= 2 \div 2 \times 1 = 1 \times 1 = 1

.\nRound bracket

= 25 \times 13 = 325

.\nNow multiply:

325 \times 1 = 325

.\nSo the correct option is (c).","solHi":"बोडमास सरलीकरण\nपहले सबसे भीतरी कोष्ठक को हल कीजिए (बोडमास)।\n16-13=3, अतः

\frac{(16 - 13)}{3} = \frac{3}{3} = 1

।\nमझला कोष्ठक

= 2 \div 2 \times 1 = 1 \times 1 = 1

।\nगोल कोष्ठक

= 25 \times 13 = 325

।\nअब गुणा कीजिए:

325 \times 1 = 325

।\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":13448,"n":48,"subject":"Elementary Mathematics","stem":"The population of a district is 372000, out of which 168000 are males. 20% of the population is literate. If 20% males are literate, then what percentage of females are literate ?","stemHi":"एक जिले की जनसंख्या 372000 है, जिसमें से 168000 पुरुष हैं। जनसंख्या का 20% साक्षर है। यदि 20% पुरुष साक्षर हैं, तो कितने प्रतिशत महिलाएँ साक्षर हैं?","context":null,"contextHi":null,"options":[{"key":"a","text":"20%","textHi":null,"imageUrl":null},{"key":"b","text":"23%","textHi":null,"imageUrl":null},{"key":"c","text":"18%","textHi":null,"imageUrl":null},{"key":"d","text":"19%","textHi":null,"imageUrl":null}],"correct":"a","sol":"$28","solHi":"प्रतिशत, साक्षरता\nमहिलाएँ =372000-168000=204000।\nकुल साक्षर =372000 का

20 % = \frac{20}{100} \times 372000 = 74400

।\nसाक्षर पुरुष =168000 का

20 % = \frac{20}{100} \times 168000 = 33600

।\nसाक्षर महिलाएँ =74400-33600=40800।\n $\"figure\"/$ \nअभीष्ट प्रतिशत

= \frac{40800}{204000} \times 100 = 20 %

।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":13449,"n":49,"subject":"Elementary Mathematics","stem":"The average age of 26 students of a class is 43 years. If the age of the teacher is also included, the average age of the whole group becomes 44 years. The age (in years) of the teacher is:","stemHi":"एक कक्षा के 26 विद्यार्थियों की औसत आयु 43 वर्ष है। यदि शिक्षक की आयु भी सम्मिलित कर ली जाए, तो पूरे समूह की औसत आयु 44 वर्ष हो जाती है। शिक्षक की आयु (वर्षों में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"68","textHi":null,"imageUrl":null},{"key":"b","text":"72","textHi":null,"imageUrl":null},{"key":"c","text":"67","textHi":null,"imageUrl":null},{"key":"d","text":"70","textHi":null,"imageUrl":null}],"correct":"d","sol":"Average, new member\nTotal age of the 26 students

= 26 \times 43 = 1118

years.\nWith the teacher there are 27 people, so their total age

= 27 \times 44 = 1188

years.\nAge of the teacher =1188-1118=70 years.\nShortcut: the teacher lifts the average of 26 others by 1 year each, so his age

= 44 + 26 \times 1 = 70

years.\nSo the correct option is (d).","solHi":"औसत, नया सदस्य\n26 विद्यार्थियों की कुल आयु

= 26 \times 43 = 1118

वर्ष।\nशिक्षक सहित 27 व्यक्ति हैं, अतः उनकी कुल आयु

= 27 \times 44 = 1188

वर्ष।\nशिक्षक की आयु =1188-1118=70 वर्ष।\nशॉर्टकट: शिक्षक अन्य 26 व्यक्तियों का औसत 1-1 वर्ष बढ़ाता है, अतः उसकी आयु

= 44 + 26 \times 1 = 70

वर्ष।\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":13450,"n":50,"subject":"Elementary Mathematics","stem":"Rodney sold 153 chairs and had a gain equal to the selling price of 63 chairs. What is his profit percentage ?","stemHi":"रॉडनी ने 153 कुर्सियाँ बेचीं और उसे 63 कुर्सियों के विक्रय मूल्य के बराबर लाभ हुआ। उसका लाभ प्रतिशत कितना है?","context":null,"contextHi":null,"options":[{"key":"a","text":"80%","textHi":null,"imageUrl":null},{"key":"b","text":"75%","textHi":null,"imageUrl":null},{"key":"c","text":"70%","textHi":null,"imageUrl":null},{"key":"d","text":"65%","textHi":null,"imageUrl":null}],"correct":"c","sol":"Profit on selling price\nTake the selling price of one chair as 1 unit, so SP of 153 chairs =153 units.\nGain = SP of 63 chairs =63 units.\nCP = SP - gain =153-63=90 units.\nProfit % = gain ÷ CP

\times 100 = \frac{63}{90} \times 100 = 70 %

.\nNote the trap: dividing 63 by 153 would give the gain on the selling price, not the profit percentage.\nSo the correct option is (c).","solHi":"विक्रय मूल्य पर लाभ\nएक कुर्सी का विक्रय मूल्य 1 इकाई मानिए, अतः 153 कुर्सियों का विक्रय मूल्य =153 इकाई।\nलाभ = 63 कुर्सियों का विक्रय मूल्य =63 इकाई।\nक्रय मूल्य = विक्रय मूल्य - लाभ =153-63=90 इकाई।\nलाभ % = लाभ ÷ क्रय मूल्य

\times 100 = \frac{63}{90} \times 100 = 70 %

।\nध्यान दीजिए: 63 में 153 का भाग देने पर विक्रय मूल्य पर लाभ मिलता, लाभ प्रतिशत नहीं।\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":13451,"n":51,"subject":"Elementary Mathematics","stem":"The salary of an employee is increased by

30 %

. By what percentage should the new salary be reduced in order to restore the original salary ? (Rounded off to 2 decimal places)","stemHi":"एक कर्मचारी का वेतन

30 %

बढ़ा दिया जाता है। मूल वेतन पुनः प्राप्त करने के लिए नए वेतन में कितने प्रतिशत की कमी की जानी चाहिए? (दो दशमलव स्थानों तक पूर्णांकित)","context":null,"contextHi":null,"options":[{"key":"a","text":"25%","textHi":null,"imageUrl":null},{"key":"b","text":"27.02%","textHi":null,"imageUrl":null},{"key":"c","text":"30%","textHi":null,"imageUrl":null},{"key":"d","text":"23.08%","textHi":null,"imageUrl":null}],"correct":"d","sol":"Percentage rise and fall\nTake the original salary as 100.\nAfter a rise of

30 %

the new salary =100+30=130.\nTo get back to 100 the new salary must fall by 130-100=30.\nThe fall is measured on the NEW salary, so reduction

% = \frac{30}{130} \times 100

.\n

= \frac{300}{13} = 23.0769 \dots \approx 23.08 %

\nSo the correct option is (d).","solHi":"प्रतिशत वृद्धि और कमी\nमूल वेतन 100 मानिए।\n

30 %

की वृद्धि के बाद नया वेतन =100+30=130।\nपुनः 100 पर लाने के लिए नए वेतन में 130-100=30 की कमी करनी होगी।\nयह कमी नए वेतन पर मापी जाती है, अतः कमी

% = \frac{30}{130} \times 100

।\n

= \frac{300}{13} = 23.0769 \dots \approx 23.08 %

\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":13452,"n":52,"subject":"Elementary Mathematics","stem":"Varun has ₹1230 with him. He divided it amongst his sons Ashish and Arun and asked them to invest it at

5 %

rate of interest compounded annually. It was seen that Ashish and Arun got same amount after 11 and 12 years respectively. How much (in ₹) did Varun give to Arun ?","stemHi":"वरुण के पास ₹1230 हैं। उसने इसे अपने पुत्रों आशीष और अरुण के बीच बाँट दिया और उनसे कहा कि वे इसे

5 %

वार्षिक चक्रवृद्धि ब्याज की दर पर निवेश करें। यह देखा गया कि आशीष और अरुण को क्रमशः 11 और 12 वर्ष बाद समान राशि प्राप्त हुई। वरुण ने अरुण को कितनी राशि (₹ में) दी?","context":null,"contextHi":null,"options":[{"key":"a","text":"600","textHi":null,"imageUrl":null},{"key":"b","text":"450","textHi":null,"imageUrl":null},{"key":"c","text":"730","textHi":null,"imageUrl":null},{"key":"d","text":"630","textHi":null,"imageUrl":null}],"correct":"a","sol":"$29","solHi":"$2a","pos":2,"neg":0.25},{"id":13453,"n":53,"subject":"Elementary Mathematics","stem":"Find the volume (in

{cm}^{3}

) of a cylinder with a diameter 6 cm and height 14 cm.","stemHi":"6 सेमी व्यास और 14 सेमी ऊँचाई वाले एक बेलन का आयतन (

{cm}^{3}

में) ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"396","textHi":null,"imageUrl":null},{"key":"b","text":"412","textHi":null,"imageUrl":null},{"key":"c","text":"376","textHi":null,"imageUrl":null},{"key":"d","text":"388","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2b","solHi":"$2c","pos":2,"neg":0.25},{"id":13454,"n":54,"subject":"Elementary Mathematics","stem":"A, B and C can do a piece of work in 15 days, 30 days and 40 days, respectively. A starts working on the first day, A and B works on the second day and

A

and

C

works on the third day. This pattern is repeated till the work gets completed. In how many days will the work be over ?","stemHi":"A, B और C किसी कार्य को क्रमशः 15 दिन, 30 दिन और 40 दिन में कर सकते हैं। पहले दिन A कार्य आरंभ करता है, दूसरे दिन A और B कार्य करते हैं तथा तीसरे दिन

A

और

C

कार्य करते हैं। यह क्रम कार्य पूरा होने तक दोहराया जाता है। कार्य कितने दिनों में समाप्त होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"

11 \frac{7}{11}

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

13 \frac{1}{4}

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

12 \frac{2}{5}

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

8 \frac{3}{5}

","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2d","solHi":"$2e","pos":2,"neg":0.25},{"id":13455,"n":55,"subject":"Elementary Mathematics","stem":"The marked price of a platinum ring is ₹52,300 and it is available for sale at two successive discounts of

20 %

and 4%. What is the selling price (in ₹) of the platinum ring ? (Round off to the nearest rupee.)","stemHi":"एक प्लैटिनम की अंगूठी का अंकित मूल्य ₹52,300 है और वह

20 %

तथा 4% की दो क्रमिक छूटों पर बिक्री के लिए उपलब्ध है। प्लैटिनम की अंगूठी का विक्रय मूल्य (₹ में) कितना है? (निकटतम रुपये तक पूर्णांकित कीजिए।)","context":null,"contextHi":null,"options":[{"key":"a","text":"40,200","textHi":null,"imageUrl":null},{"key":"b","text":"40,033","textHi":null,"imageUrl":null},{"key":"c","text":"40,166","textHi":null,"imageUrl":null},{"key":"d","text":"40,233","textHi":null,"imageUrl":null}],"correct":"c","sol":"$2f","solHi":"$30","pos":2,"neg":0.25},{"id":13456,"n":56,"subject":"Elementary Mathematics","stem":"A shopkeeper bought an article for ₹540. At what price (in ₹) should he sell the article to make

10 %

profit ?","stemHi":"एक दुकानदार ने एक वस्तु ₹540 में खरीदी।

10 %

लाभ कमाने के लिए उसे वह वस्तु किस मूल्य (₹ में) पर बेचनी चाहिए?","context":null,"contextHi":null,"options":[{"key":"a","text":"606","textHi":null,"imageUrl":null},{"key":"b","text":"594","textHi":null,"imageUrl":null},{"key":"c","text":"582","textHi":null,"imageUrl":null},{"key":"d","text":"486","textHi":null,"imageUrl":null}],"correct":"b","sol":"Profit percentage\nSP = CP

\times (1 + \frac{profit}{100})

, with profit =10.\n

= 540 \times (1 + \frac{10}{100}) = 540 \times \frac{110}{100}

\n=594\nSo the article must be sold for ₹594, i.e. option (b).","solHi":"लाभ प्रतिशत\nविक्रय मूल्य = क्रय मूल्य

\times (1 + \frac{profit}{100})

, जहाँ लाभ =10।\n

= 540 \times (1 + \frac{10}{100}) = 540 \times \frac{110}{100}

\n=594\nअतः वस्तु ₹594 में बेचनी होगी, अर्थात् विकल्प (b)।","pos":2,"neg":0.25},{"id":13457,"n":57,"subject":"Elementary Mathematics","stem":"The force acting on an object is directly proportional to its mass. If a force of 10 N is required to move an object of mass 2 kg , what force (in newtons) is needed to move an object of mass 5 kg ?","stemHi":"किसी वस्तु पर लगने वाला बल उसके द्रव्यमान के सीधे अनुपात में होता है। यदि 2 किग्रा द्रव्यमान की वस्तु को गति देने के लिए 10 N बल की आवश्यकता है, तो 5 किग्रा द्रव्यमान की वस्तु को गति देने के लिए कितने बल (न्यूटन में) की आवश्यकता होगी?","context":null,"contextHi":null,"options":[{"key":"a","text":"25","textHi":null,"imageUrl":null},{"key":"b","text":"30","textHi":null,"imageUrl":null},{"key":"c","text":"20","textHi":null,"imageUrl":null},{"key":"d","text":"15","textHi":null,"imageUrl":null}],"correct":"a","sol":"$31","solHi":"$32","pos":2,"neg":0.25},{"id":13458,"n":58,"subject":"Elementary Mathematics","stem":"Two trains having lengths of 450 m and 350 m are running at speeds of 80

km / h

and

110 km / h

, respectively, in the same direction. The time taken (in minutes) by the faster train, coming from behind, to completely cross the other train is:","stemHi":"450 मी और 350 मी लंबाई वाली दो रेलगाड़ियाँ क्रमशः 80

km / h

और

110 km / h

की चाल से एक ही दिशा में चल रही हैं। पीछे से आ रही तेज़ रेलगाड़ी को दूसरी रेलगाड़ी को पूरी तरह पार करने में लगने वाला समय (मिनटों में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"2.4","textHi":null,"imageUrl":null},{"key":"b","text":"3.4","textHi":null,"imageUrl":null},{"key":"c","text":"1.6","textHi":null,"imageUrl":null},{"key":"d","text":"3","textHi":null,"imageUrl":null}],"correct":"c","sol":"$33","solHi":"$34","pos":2,"neg":0.25},{"id":13459,"n":59,"subject":"Elementary Mathematics","stem":"Rakesh invests a sum of ₹5400 and Shivam invests a sum of ₹10200 at the same rate of simple interest per annum. If, at the end of 4 years, Shivam gets ₹480 more interest than Rakesh, then find the rate of interest per annum (in percentage).","stemHi":"राकेश ₹5400 की राशि और शिवम ₹10200 की राशि समान वार्षिक साधारण ब्याज दर पर निवेश करते हैं। यदि 4 वर्ष के अंत में शिवम को राकेश से ₹480 अधिक ब्याज मिलता है, तो वार्षिक ब्याज दर (प्रतिशत में) ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"2.5","textHi":null,"imageUrl":null},{"key":"b","text":"3.5","textHi":null,"imageUrl":null},{"key":"c","text":"1.5","textHi":null,"imageUrl":null},{"key":"d","text":"4.5","textHi":null,"imageUrl":null}],"correct":"a","sol":"Simple interest, rate\nSimple interest

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

, and here R and T=4 are the same for both men.\nSo the extra interest comes only from the extra principal.\nExtra principal =10200-5400=₹4800.\n

\frac{4800 \times R \times 4}{100} = 480

\n192R=480\n

R = \frac{480}{192} = 2.5

\nSo the rate is

2.5 %

per annum, i.e. option (a).","solHi":"साधारण ब्याज, दर\nसाधारण ब्याज

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

, और यहाँ दोनों के लिए R तथा T=4 समान हैं।\nअतः अतिरिक्त ब्याज केवल अतिरिक्त मूलधन से आता है।\nअतिरिक्त मूलधन =10200-5400=₹4800।\n

\frac{4800 \times R \times 4}{100} = 480

\n192R=480\n

R = \frac{480}{192} = 2.5

\nअतः दर

2.5 %

वार्षिक है, अर्थात् विकल्प (a)।","pos":2,"neg":0.25},{"id":13460,"n":60,"subject":"Elementary Mathematics","stem":"Veer has ₹1632 with him. He divided it amongst his sons Nitin and Pravin and asked them to invest it at 4% rate of interest compounded annually. It was seen that Nitin and Pravin got same amount after 12 and 13 years respectively. How much (in ₹) did Veer give to Nitin ?","stemHi":"वीर के पास ₹1632 हैं। उसने इसे अपने पुत्रों नितिन और प्रवीण के बीच बाँट दिया और उनसे कहा कि वे इसे 4% वार्षिक चक्रवृद्धि ब्याज की दर पर निवेश करें। यह देखा गया कि नितिन और प्रवीण को क्रमशः 12 और 13 वर्ष बाद समान राशि प्राप्त हुई। वीर ने नितिन को कितनी राशि (₹ में) दी?","context":null,"contextHi":null,"options":[{"key":"a","text":"800","textHi":null,"imageUrl":null},{"key":"b","text":"832","textHi":null,"imageUrl":null},{"key":"c","text":"682","textHi":null,"imageUrl":null},{"key":"d","text":"900","textHi":null,"imageUrl":null}],"correct":"b","sol":"$35","solHi":"$36","pos":2,"neg":0.25}],"test":{"slug":"ssc-gd-constable--17-feb-2025-shift-3-maths","title":"SSC GD Constable 17 February 2025 Shift-3 — Elementary Mathematics Sectional Test","examName":"SSC GD","paperLabel":"17 February 2025 · Shift 3","sectionSubject":"Elementary Mathematics","durationMinutes":15,"format":"sectional_test"}}]