26:I[81166,["/_next/static/immutable/chunks/2corl6wyj4669.js","/_next/static/immutable/chunks/38n271cv4vmyv.js","/_next/static/immutable/chunks/2pf73jja2520w.js"],"default"] 27:T7bc,Work with alternating helpers Take the total work as the LCM of 30, 33, 36 and 44, i.e. 1980 units. One day's work:

A = \frac{1980}{30} = 66

B = \frac{1980}{33} = 60

C = \frac{1980}{36} = 55

D = \frac{1980}{44} = 45

units. A and B together do 66+60=126 units a day, and the helper changes every two days.

One full cycle of 4 days does 362+342=704 units, so 8 days (two cycles) do 1408 units. Days 9 and 10 are C days: 1408+362=1770 units done, so 1980-1770=210 units are left. Day 11 is a D day and gives 171 units, leaving 210-171=39 units. Day 12 is also a D day, so the last bit needs

\frac{39}{171} = \frac{13}{57}

of a day. Total time

= 11 + \frac{13}{57} = 11 \frac{13}{57}

days. Hence the correct option is (c).28:Taa4,बारी-बारी सहायकों वाला कार्य कुल कार्य को 30, 33, 36 और 44 का लघुत्तम समापवर्त्य अर्थात् 1980 इकाई मानिए। एक दिन का कार्य:

A = \frac{1980}{30} = 66

B = \frac{1980}{33} = 60

C = \frac{1980}{36} = 55

D = \frac{1980}{44} = 45

इकाई। A और B मिलकर प्रतिदिन 66+60=126 इकाई कार्य करते हैं तथा सहायक हर दो दिन में बदलता है।

4 दिन का एक पूरा चक्र 362+342=704 इकाई कार्य करता है, अतः 8 दिन (दो चक्र) में 1408 इकाई कार्य होता है। 9वाँ और 10वाँ दिन C के दिन हैं: 1408+362=1770 इकाई कार्य पूर्ण, अतः 1980-1770=210 इकाई शेष। 11वाँ दिन D का दिन है और उसमें 171 इकाई कार्य होता है, शेष 210-171=39 इकाई। 12वाँ दिन भी D का दिन है, अतः अंतिम भाग में

\frac{39}{171} = \frac{13}{57}

दिन लगेगा। कुल समय

= 11 + \frac{13}{57} = 11 \frac{13}{57}

दिन। इसलिए सही विकल्प (c) है।29:T52f,Melting and recasting a cube Melting changes the shape but not the volume, so the big cube's volume equals the total volume of the 8 small cubes. Volume of the big cube

= 9^{3} = 729

cm³.

Let the side of a small cube be a, so

8 a^{3} = 729

a^{3} = \frac{729}{8}

a = \sqrt[3]{\frac{729}{8}} = \frac{9}{2} = 4.5

Hence each small cube has a side of 4.5 cm, option (b).2a:T648,घन को पिघलाकर पुनः ढालना पिघलाने से आकार बदलता है, आयतन नहीं, अतः बड़े घन का आयतन 8 छोटे घनों के कुल आयतन के बराबर होता है। बड़े घन का आयतन

= 9^{3} = 729

cm³।

माना कि छोटे घन की भुजा a है, तो

8 a^{3} = 729

।

a^{3} = \frac{729}{8}

a = \sqrt[3]{\frac{729}{8}} = \frac{9}{2} = 4.5

अतः प्रत्येक छोटे घन की भुजा 4.5 cm है, विकल्प (b)।2b:T4c3,Speed for the remaining distance Total time =2 hours 24 minutes

= 2 + \frac{24}{60} = 2.4

hours. One-third of 24 km =8 km, and this part is covered at 8 km/hr. Time for the first part

= \frac{8}{8} = 1

hour.

Remaining distance =24-8=16 km and remaining time =2.4-1=1.4 hours. Required speed

= \frac{16}{1.4} = \frac{160}{14} = \frac{80}{7} = 11 \frac{3}{7}

km/hr. Hence the correct option is (a).2c:T5a0,शेष दूरी की चाल कुल समय =2 घंटे 24 मिनट

= 2 + \frac{24}{60} = 2.4

घंटे। 24 km का एक-तिहाई =8 km, और यह भाग 8 km/hr की चाल से तय किया जाता है। पहले भाग में लगा समय

= \frac{8}{8} = 1

घंटा।

शेष दूरी =24-8=16 km तथा शेष समय =2.4-1=1.4 घंटे। अभीष्ट चाल

= \frac{16}{1.4} = \frac{160}{14} = \frac{80}{7} = 11 \frac{3}{7}

km/hr। इसलिए सही विकल्प (a) है।2d:T6a9,Compound interest to simple interest The two interests share the same principal, rate and time, so first find the principal from the compound interest. For 2 years, CI

= P ({(1 + \frac{R}{100})}^{2} - 1)

229.5 = P ({(1.04)}^{2} - 1) = P \times 0.0816

P = \frac{229.5}{0.0816} = 2812.5

= \frac{P \times R \times T}{100} = \frac{2812.5 \times 4 \times 2}{100} = 225

Check: for 2 years CI - SI = 4% of the first year's interest

= 0.04 \times 112.5 = 4.5

, and 225+4.5=229.5. Hence the simple interest is ₹225, option (b).2e:T848,चक्रवृद्धि से साधारण ब्याज दोनों ब्याजों का मूलधन, दर और समय एक ही है, अतः पहले चक्रवृद्धि ब्याज से मूलधन ज्ञात कीजिए। 2 वर्ष के लिए, चक्रवृद्धि ब्याज

= P ({(1 + \frac{R}{100})}^{2} - 1)

।

229.5 = P ({(1.04)}^{2} - 1) = P \times 0.0816

P = \frac{229.5}{0.0816} = 2812.5

साधारण ब्याज

= \frac{P \times R \times T}{100} = \frac{2812.5 \times 4 \times 2}{100} = 225

जाँच: 2 वर्ष में चक्रवृद्धि ब्याज - साधारण ब्याज = पहले वर्ष के ब्याज का 4%

= 0.04 \times 112.5 = 4.5

, और 225+4.5=229.5। अतः साधारण ब्याज ₹225 है, विकल्प (b)।2f:T4d3,Trains crossing in the same direction For two trains moving in the same direction the relative speed is the difference: 90-60=30 km/h. 30 km/h

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

m/s.

To cross completely, the faster train has to cover the sum of the two lengths =210+440=650 m. Time

= \frac{650}{\frac{25}{3}} = 650 \times \frac{3}{25} = 78

seconds. 78 seconds

= \frac{78}{60} = 1.3

minutes. Hence the correct option is (a).30:T628,एक ही दिशा में रेलगाड़ियों का पार करना एक ही दिशा में चलती दो रेलगाड़ियों की सापेक्ष चाल उनका अंतर होती है: 90-60=30 km/h। 30 km/h

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

m/s।

पूरी तरह पार करने के लिए तेज़ रेलगाड़ी को दोनों लंबाइयों का योग =210+440=650 m तय करना होगा। समय

= \frac{650}{\frac{25}{3}} = 650 \times \frac{3}{25} = 78

सेकंड। 78 सेकंड

= \frac{78}{60} = 1.3

मिनट। इसलिए सही विकल्प (a) है।31:T6ba,Compounding over 10-month periods Interest is added every 10 months, so one conversion period is 10 months, not one year. Rate for one period

= 12 % \times \frac{10}{12} = 10 %

2 \frac{1}{2}

years =30 months, which is

\frac{30}{10} = 3

periods.

A = x {(1 + \frac{10}{100})}^{3}

75867 = x \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} = x \times \frac{1331}{1000}

x = \frac{75867 \times 1000}{1331} = 57000

Hence the correct option is (d).32:T7b6,10-10 माह पर चक्रवृद्धि ब्याज प्रत्येक 10 महीने बाद जोड़ा जाता है, अतः एक संयोजन अवधि 10 महीने की है, एक वर्ष की नहीं। एक अवधि की दर

= 12 % \times \frac{10}{12} = 10 %

।

2 \frac{1}{2}

वर्ष =30 महीने, अर्थात्

\frac{30}{10} = 3

अवधियाँ।

A = x {(1 + \frac{10}{100})}^{3}

75867 = x \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} = x \times \frac{1331}{1000}

x = \frac{75867 \times 1000}{1331} = 57000

इसलिए सही विकल्प (d) है।1c:["$","$L26",null,{"mode":"practice","dropped":0,"bilingual":true,"choiceSubjects":[],"questions":[{"id":4541,"n":41,"subject":"Elementary Mathematics","stem":"A's and B's salaries are respectively 40% and 70% rupees more than C's salary. What is the ratio of B's salary to A's salary ?","stemHi":"A और B का वेतन क्रमशः C के वेतन से 40% और 70% अधिक है। B के वेतन का A के वेतन से अनुपात क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"17 : 14","textHi":null,"imageUrl":null},{"key":"b","text":"18 : 13","textHi":null,"imageUrl":null},{"key":"c","text":"9 : 5","textHi":null,"imageUrl":null},{"key":"d","text":"23 : 20","textHi":null,"imageUrl":null}],"correct":"a","sol":"Percentage to ratio\nBoth salaries are compared with C's salary, so make C's salary the base.\nLet C's salary be 100 units.\nA is 40% more than C, so A =100+40=140 units.\nB is 70% more than C, so B =100+70=170 units.\nB:A=170:140=17:14 (dividing both terms by 10).\nHence the correct option is (a).","solHi":"प्रतिशत से अनुपात\nदोनों वेतनों की तुलना C के वेतन से की गई है, अतः C के वेतन को आधार मानिए।\nमाना कि C का वेतन 100 इकाई है।\nA, C से 40% अधिक है, अतः A =100+40=140 इकाई।\nB, C से 70% अधिक है, अतः B =100+70=170 इकाई।\nB:A=170:140=17:14 (दोनों पदों में 10 से भाग देने पर)।\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":4542,"n":42,"subject":"Elementary Mathematics","stem":"While selling 15 balls for ₹1,220, there is loss equal to the cost price of 5 balls. The cost price (in ₹) of one ball is:","stemHi":"15 गेंदों को ₹1,220 में बेचने पर 5 गेंदों के क्रय मूल्य के बराबर हानि होती है। एक गेंद का क्रय मूल्य (₹ में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"145","textHi":null,"imageUrl":null},{"key":"b","text":"122","textHi":null,"imageUrl":null},{"key":"c","text":"112","textHi":null,"imageUrl":null},{"key":"d","text":"120","textHi":null,"imageUrl":null}],"correct":"b","sol":"Loss stated in units\nLet the cost price of one ball be x (in ₹).\nCost price of 15 balls =15x and selling price of 15 balls =1220.\nLoss = CP - SP =15x-1220, and the question says this loss equals the CP of 5 balls =5x.\n15x-1220=5x\n10x=1220\n

x = \frac{1220}{10} = 122

\nHence the cost price of one ball is ₹122, option (b).","solHi":"वस्तुओं में व्यक्त हानि\nमाना कि एक गेंद का क्रय मूल्य x (₹ में) है।\n15 गेंदों का क्रय मूल्य =15x तथा 15 गेंदों का विक्रय मूल्य =1220।\nहानि = क्रय मूल्य - विक्रय मूल्य =15x-1220, और प्रश्नानुसार यह हानि 5 गेंदों के क्रय मूल्य =5x के बराबर है।\n15x-1220=5x\n10x=1220\n

x = \frac{1220}{10} = 122

\nअतः एक गेंद का क्रय मूल्य ₹122 है, विकल्प (b)।","pos":2,"neg":0.25},{"id":4543,"n":43,"subject":"Elementary Mathematics","stem":"If

2 %

x = 360

, then

x

is equal to:","stemHi":"यदि

2 %

x = 360

है, तो

x

बराबर है:","context":null,"contextHi":null,"options":[{"key":"a","text":"36100","textHi":null,"imageUrl":null},{"key":"b","text":"36000","textHi":null,"imageUrl":null},{"key":"c","text":"18000","textHi":null,"imageUrl":null},{"key":"d","text":"18100","textHi":null,"imageUrl":null}],"correct":"c","sol":"Basic percentage\n'2% of x' means

\frac{2}{100} \times x

.\n

\frac{2}{100} \times x = 360

x = 360 \times \frac{100}{2}

x = 360 \times 50 = 18000

\nHence the correct option is (c).","solHi":"मूल प्रतिशत\n'x का 2%' का अर्थ है

\frac{2}{100} \times x

।\n

\frac{2}{100} \times x = 360

x = 360 \times \frac{100}{2}

x = 360 \times 50 = 18000

\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":4544,"n":44,"subject":"Elementary Mathematics","stem":"A, B, C and D can do a piece of work separately in 30 days, 33 days, 36 days and 44 days, respectively. In how many days can A and B together complete the work, if A and B together are assisted by C and D on alternate two-two days starting with C for first two days, then D on next two days and again C on next two days and so on ?","stemHi":"A, B, C और D किसी कार्य को अलग-अलग क्रमशः 30 दिन, 33 दिन, 36 दिन और 44 दिन में कर सकते हैं। यदि A और B मिलकर कार्य करते हैं तथा C और D बारी-बारी से दो-दो दिन उनकी सहायता करते हैं - पहले दो दिन C, अगले दो दिन D, फिर अगले दो दिन C और इसी प्रकार आगे - तो A और B मिलकर कार्य को कितने दिन में पूरा करेंगे?","context":null,"contextHi":null,"options":[{"key":"a","text":"

6 \frac{7}{24}

days","textHi":"

6 \frac{7}{24}

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

8 \frac{5}{36}

days","textHi":"

8 \frac{5}{36}

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

11 \frac{13}{57}

days","textHi":"

11 \frac{13}{57}

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

5 \frac{5}{11}

days","textHi":"

5 \frac{5}{11}

दिन","imageUrl":null}],"correct":"c","sol":"$27","solHi":"$28","pos":2,"neg":0.25},{"id":4545,"n":45,"subject":"Elementary Mathematics","stem":"The value of

79 - 10 \times [2 + 3 \times {12

- 6 (6 - 5) \times 2} \div 20

] is:","stemHi":"

79 - 10 \times [2 + 3 \times {12

- 6 (6 - 5) \times 2} \div 20

] का मान है:","context":null,"contextHi":null,"options":[{"key":"a","text":"59","textHi":null,"imageUrl":null},{"key":"b","text":"63","textHi":null,"imageUrl":null},{"key":"c","text":"55","textHi":null,"imageUrl":null},{"key":"d","text":"57","textHi":null,"imageUrl":null}],"correct":"a","sol":"BODMAS with brackets\nOpen the brackets from the inside out: round, then curly, then square.\nRound bracket: 6-5=1, so

6 (6 - 5) \times 2 = 6 \times 1 \times 2 = 12

.\nCurly bracket:

{12 - 12} = 0

.\nNow

3 \times 0 \div 20 = 0

, so the square bracket becomes [2+0]=2.\n

79 - 10 \times 2 = 79 - 20 = 59

\nHence the correct option is (a).","solHi":"कोष्ठक सहित BODMAS\nकोष्ठकों को अंदर से बाहर की ओर हल कीजिए: पहले लघु, फिर मझला, फिर बड़ा कोष्ठक।\nलघु कोष्ठक: 6-5=1, अतः

6 (6 - 5) \times 2 = 6 \times 1 \times 2 = 12

।\nमझला कोष्ठक:

{12 - 12} = 0

।\nअब

3 \times 0 \div 20 = 0

, अतः बड़ा कोष्ठक [2+0]=2 हो जाता है।\n

79 - 10 \times 2 = 79 - 20 = 59

\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":4546,"n":46,"subject":"Elementary Mathematics","stem":"A merchant fixes the marked price of his goods at 50% above the cost price. He sells his goods at 12% discount. His percentage of profit is:","stemHi":"एक व्यापारी अपने सामान का अंकित मूल्य क्रय मूल्य से 50% अधिक रखता है। वह अपना सामान 12% छूट पर बेचता है। उसका लाभ प्रतिशत है:","context":null,"contextHi":null,"options":[{"key":"a","text":"

37 %

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

32 %

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

43 %

","textHi":null,"imageUrl":null},{"key":"d","text":"35%","textHi":null,"imageUrl":null}],"correct":"b","sol":"Marked price, discount, profit\nTake the cost price as 100 units, because both percentages are easy on 100.\nMarked price =100+50=150 units.\nThe 12% discount is on the marked price, not on the cost price, so SP

= 150 \times \frac{88}{100} = 132

units.\nProfit =132-100=32 units.\nProfit

% = \frac{32}{100} \times 100 = 32 %

\nHence the correct option is (b).","solHi":"अंकित मूल्य, छूट, लाभ\nक्रय मूल्य को 100 इकाई मानिए, क्योंकि दोनों प्रतिशत 100 पर सरल हो जाते हैं।\nअंकित मूल्य =100+50=150 इकाई।\n12% की छूट अंकित मूल्य पर है, क्रय मूल्य पर नहीं, अतः विक्रय मूल्य

= 150 \times \frac{88}{100} = 132

इकाई।\nलाभ =132-100=32 इकाई।\nलाभ

% = \frac{32}{100} \times 100 = 32 %

\nइसलिए सही विकल्प (b) है।","pos":2,"neg":0.25},{"id":4547,"n":47,"subject":"Elementary Mathematics","stem":"Evaluate:

2 - [3 - {6 - (6 - 4 + 6)}]

","stemHi":"मान ज्ञात कीजिए:

2 - [3 - {6 - (6 - 4 + 6)}]

","context":null,"contextHi":null,"options":[{"key":"a","text":"2","textHi":null,"imageUrl":null},{"key":"b","text":"-3","textHi":null,"imageUrl":null},{"key":"c","text":"-6","textHi":null,"imageUrl":null},{"key":"d","text":"0","textHi":null,"imageUrl":null}],"correct":"b","sol":"Simplification of brackets\nInnermost round bracket first: 6-4+6=8.\nCurly bracket:

{6 - 8} = - 2

.\nSquare bracket: [3-(-2)]=3+2=5.\n2-5=-3\nHence the correct option is (b).","solHi":"कोष्ठकों का सरलीकरण\nसबसे भीतरी लघु कोष्ठक पहले: 6-4+6=8।\nमझला कोष्ठक:

{6 - 8} = - 2

।\nबड़ा कोष्ठक: [3-(-2)]=3+2=5।\n2-5=-3\nइसलिए सही विकल्प (b) है।","pos":2,"neg":0.25},{"id":4548,"n":48,"subject":"Elementary Mathematics","stem":"A cube of side 9 cm made of iron is melted and recast into 8 small cubes. Find the side (in cm ) of each small cube.","stemHi":"लोहे से बने 9 cm भुजा वाले एक घन को पिघलाकर 8 छोटे घन बनाए जाते हैं। प्रत्येक छोटे घन की भुजा (cm में) ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"4","textHi":null,"imageUrl":null},{"key":"b","text":"4.5","textHi":null,"imageUrl":null},{"key":"c","text":"5.5","textHi":null,"imageUrl":null},{"key":"d","text":"5","textHi":null,"imageUrl":null}],"correct":"b","sol":"$29","solHi":"$2a","pos":2,"neg":0.25},{"id":4549,"n":49,"subject":"Elementary Mathematics","stem":"Find the value of\n

((36 \div 9) \times (\frac{56}{8} + \frac{14}{1} \times (6 - 5)))

","stemHi":"मान ज्ञात कीजिए\n

((36 \div 9) \times (\frac{56}{8} + \frac{14}{1} \times (6 - 5)))

","context":null,"contextHi":null,"options":[{"key":"a","text":"84","textHi":null,"imageUrl":null},{"key":"b","text":"81","textHi":null,"imageUrl":null},{"key":"c","text":"78","textHi":null,"imageUrl":null},{"key":"d","text":"98","textHi":null,"imageUrl":null}],"correct":"a","sol":"Order of operations\nInnermost bracket first: 6-5=1.\nCurly bracket:

\frac{56}{8} + \frac{14}{1} \times 1 = 7 + 14 = 21

.\nRound bracket:

36 \div 9 = 4

.\n

(4 \times 21) = 84

\nHence the correct option is (a).","solHi":"संक्रियाओं का क्रम\nसबसे भीतरी कोष्ठक पहले: 6-5=1।\nमझला कोष्ठक:

\frac{56}{8} + \frac{14}{1} \times 1 = 7 + 14 = 21

।\nलघु कोष्ठक:

36 \div 9 = 4

।\n

(4 \times 21) = 84

\nइसलिए सही विकल्प (a) है।","pos":2,"neg":0.25},{"id":4550,"n":50,"subject":"Elementary Mathematics","stem":"The average age of 28 students of a class is 40 years. If the age of the teacher is also included, the average age of the whole group becomes 41 years. The age (in years) of the teacher is:","stemHi":"एक कक्षा के 28 विद्यार्थियों की औसत आयु 40 वर्ष है। यदि शिक्षक की आयु भी सम्मिलित कर ली जाए, तो पूरे समूह की औसत आयु 41 वर्ष हो जाती है। शिक्षक की आयु (वर्षों में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"74","textHi":null,"imageUrl":null},{"key":"b","text":"67","textHi":null,"imageUrl":null},{"key":"c","text":"70","textHi":null,"imageUrl":null},{"key":"d","text":"69","textHi":null,"imageUrl":null}],"correct":"d","sol":"Average and a new member\nTotal age of the 28 students

= 28 \times 40 = 1120

years.\nWith the teacher the group has 29 people, so their total age

= 29 \times 41 = 1189

years.\nAge of the teacher =1189-1120=69 years.\nShortcut: the teacher's age = new average + (number of students

\times

rise in average)

= 41 + 28 \times 1 = 69

.\nHence the correct option is (d).","solHi":"औसत और नया सदस्य\n28 विद्यार्थियों की कुल आयु

= 28 \times 40 = 1120

वर्ष।\nशिक्षक सहित समूह में 29 व्यक्ति हैं, अतः उनकी कुल आयु

= 29 \times 41 = 1189

वर्ष।\nशिक्षक की आयु =1189-1120=69 वर्ष।\nशॉर्टकट: शिक्षक की आयु = नया औसत + (विद्यार्थियों की संख्या

\times

औसत में वृद्धि)

= 41 + 28 \times 1 = 69

।\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":4551,"n":51,"subject":"Elementary Mathematics","stem":"Ravi decided to cover a distance of 24 km in 2 hours 24 minutes. Further he decided to cover the initial one-third of the total distance at

8 km / hr

and the remaining at some different speed. What is the speed (in km/hr) of Ravi after one-third distance is covered?","stemHi":"रवि ने 24 km की दूरी 2 घंटे 24 मिनट में तय करने का निश्चय किया। आगे उसने कुल दूरी का प्रारंभिक एक-तिहाई भाग

8 km / hr

की चाल से तथा शेष दूरी किसी भिन्न चाल से तय करने का निश्चय किया। एक-तिहाई दूरी तय कर लेने के बाद रवि की चाल (km/hr में) क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"

11 \frac{3}{7}

","textHi":null,"imageUrl":null},{"key":"b","text":"12","textHi":null,"imageUrl":null},{"key":"c","text":"

12 \frac{3}{7}

","textHi":null,"imageUrl":null},{"key":"d","text":"11","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2b","solHi":"$2c","pos":2,"neg":0.25},{"id":4552,"n":52,"subject":"Elementary Mathematics","stem":"Evaluate:

32 \div 8 \times 4 - 2 \times 3

","stemHi":"मान ज्ञात कीजिए:

32 \div 8 \times 4 - 2 \times 3

","context":null,"contextHi":null,"options":[{"key":"a","text":"9","textHi":null,"imageUrl":null},{"key":"b","text":"12","textHi":null,"imageUrl":null},{"key":"c","text":"13","textHi":null,"imageUrl":null},{"key":"d","text":"10","textHi":null,"imageUrl":null}],"correct":"d","sol":"BODMAS left to right\nDivision and multiplication rank equally, so they are done left to right, before the subtraction.\n

32 \div 8 \times 4 = 4 \times 4 = 16

2 \times 3 = 6

\n16-6=10\nHence the correct option is (d).","solHi":"BODMAS बाएँ से दाएँ\nभाग और गुणा का स्तर समान होता है, अतः इन्हें घटाने से पहले बाएँ से दाएँ किया जाता है।\n

32 \div 8 \times 4 = 4 \times 4 = 16

2 \times 3 = 6

\n16-6=10\nइसलिए सही विकल्प (d) है।","pos":2,"neg":0.25},{"id":4553,"n":53,"subject":"Elementary Mathematics","stem":"The students in the three sections A, B and C of Class X are in the ratio 5 : 4 : 7. If 15, 16 and 9 new students are admitted to sections A, B and C, respectively, the ratio changes to 10 : 9 : 11. What is the total number of students in Class

X

after the new admissions?","stemHi":"कक्षा X के तीन वर्गों A, B और C के विद्यार्थी 5 : 4 : 7 के अनुपात में हैं। यदि वर्ग A, B और C में क्रमशः 15, 16 और 9 नए विद्यार्थी प्रवेश लेते हैं, तो अनुपात बदलकर 10 : 9 : 11 हो जाता है। नए प्रवेशों के बाद कक्षा

X

में विद्यार्थियों की कुल संख्या क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"210","textHi":null,"imageUrl":null},{"key":"b","text":"120","textHi":null,"imageUrl":null},{"key":"c","text":"150","textHi":null,"imageUrl":null},{"key":"d","text":"90","textHi":null,"imageUrl":null}],"correct":"b","sol":"Ratio after new admissions\nLet the sections hold 5x, 4x and 7x students.\nAfter the admissions they hold 5x+15, 4x+16 and 7x+9, and these are in the ratio 10:9:11.\nTwo of the three parts are enough:

\frac{5 x + 15}{4 x + 16} = \frac{10}{9}

.\n9(5x+15)=10(4x+16)\n45x+135=40x+160\n5x=25, so x=5.\n $\"figure\"/$ \nThe third part checks out too, since 40:36:44=10:9:11.\nTotal =40+36+44=120\nHence the correct option is (b).","solHi":"नए प्रवेशों के बाद अनुपात\nमाना कि वर्गों में क्रमशः 5x, 4x और 7x विद्यार्थी हैं।\nप्रवेशों के बाद उनमें 5x+15, 4x+16 और 7x+9 विद्यार्थी हैं, और ये 10:9:11 के अनुपात में हैं।\nतीन में से दो भाग ही पर्याप्त हैं:

\frac{5 x + 15}{4 x + 16} = \frac{10}{9}

।\n9(5x+15)=10(4x+16)\n45x+135=40x+160\n5x=25, अतः x=5।\n $\"figure\"/$ \nतीसरा भाग भी सत्यापित हो जाता है, क्योंकि 40:36:44=10:9:11।\nकुल =40+36+44=120\nइसलिए सही विकल्प (b) है।","pos":2,"neg":0.25},{"id":4554,"n":54,"subject":"Elementary Mathematics","stem":"Yogesh invested some money in HDFC at 4% per annum rate of interest. What would be the corresponding simple interest (in ₹) if after 2 years, Yogesh got ₹229.5 as compound interest, considering annual compounding ?","stemHi":"योगेश ने HDFC में 4% वार्षिक ब्याज दर पर कुछ धन निवेश किया। यदि 2 वर्ष बाद, वार्षिक संयोजन मानते हुए, योगेश को ₹229.5 चक्रवृद्धि ब्याज मिला, तो तत्संबंधी साधारण ब्याज (₹ में) क्या होगा?","context":null,"contextHi":null,"options":[{"key":"a","text":"235","textHi":null,"imageUrl":null},{"key":"b","text":"225","textHi":null,"imageUrl":null},{"key":"c","text":"240","textHi":null,"imageUrl":null},{"key":"d","text":"220","textHi":null,"imageUrl":null}],"correct":"b","sol":"$2d","solHi":"$2e","pos":2,"neg":0.25},{"id":4555,"n":55,"subject":"Elementary Mathematics","stem":"Rakesh sold 150 chairs and had a gain equal to the selling price of 75 chairs. What is his profit percentage?","stemHi":"राकेश ने 150 कुर्सियाँ बेचीं और उसे 75 कुर्सियों के विक्रय मूल्य के बराबर लाभ हुआ। उसका लाभ प्रतिशत क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"110%","textHi":null,"imageUrl":null},{"key":"b","text":"95%","textHi":null,"imageUrl":null},{"key":"c","text":"100%","textHi":null,"imageUrl":null},{"key":"d","text":"105%","textHi":null,"imageUrl":null}],"correct":"c","sol":"Gain given as selling price\nLet the selling price of one chair be s and its cost price be c.\nGain on 150 chairs =150s-150c, and this equals the SP of 75 chairs =75s.\n150s-150c=75s\n75s=150c, so s=2c.\nProfit on one chair =2c-c=c, so profit

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

.\nHence the correct option is (c).","solHi":"विक्रय मूल्य में दिया गया लाभ\nमाना कि एक कुर्सी का विक्रय मूल्य s और क्रय मूल्य c है।\n150 कुर्सियों पर लाभ =150s-150c, और यह 75 कुर्सियों के विक्रय मूल्य =75s के बराबर है।\n150s-150c=75s\n75s=150c, अतः s=2c।\nएक कुर्सी पर लाभ =2c-c=c, अतः लाभ

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

।\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":4556,"n":56,"subject":"Elementary Mathematics","stem":"12 chairs and 6 tables were bought for ₹12,600. If the average cost of a table is ₹1,500, then find the average cost of a chair.","stemHi":"12 कुर्सियाँ और 6 मेजें ₹12,600 में खरीदी गईं। यदि एक मेज़ की औसत लागत ₹1,500 है, तो एक कुर्सी की औसत लागत ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"₹350","textHi":null,"imageUrl":null},{"key":"b","text":"₹500","textHi":null,"imageUrl":null},{"key":"c","text":"₹250","textHi":null,"imageUrl":null},{"key":"d","text":"₹300","textHi":null,"imageUrl":null}],"correct":"d","sol":"Average cost from a total\nCost of 6 tables

= 6 \times 1500 = 9000

.\nSo the 12 chairs together cost 12600-9000=3600.\nAverage cost of one chair

= \frac{3600}{12} = 300

.\nHence the average cost of a chair is ₹300, option (d).","solHi":"कुल लागत से औसत\n6 मेजों की लागत

= 6 \times 1500 = 9000

।\nअतः 12 कुर्सियों की कुल लागत =12600-9000=3600।\nएक कुर्सी की औसत लागत

= \frac{3600}{12} = 300

।\nअतः एक कुर्सी की औसत लागत ₹300 है, विकल्प (d)।","pos":2,"neg":0.25},{"id":4557,"n":57,"subject":"Elementary Mathematics","stem":"The population of a district is 327000, out of which 224000 are males. 65% of the population is literate. If 65% males are literate, then what percentage of females are literate?","stemHi":"एक जिले की जनसंख्या 327000 है, जिनमें से 224000 पुरुष हैं। जनसंख्या का 65% साक्षर है। यदि 65% पुरुष साक्षर हैं, तो कितने प्रतिशत महिलाएँ साक्षर हैं?","context":null,"contextHi":null,"options":[{"key":"a","text":"68%","textHi":null,"imageUrl":null},{"key":"b","text":"

67 %

","textHi":null,"imageUrl":null},{"key":"c","text":"65%","textHi":null,"imageUrl":null},{"key":"d","text":"66%","textHi":null,"imageUrl":null}],"correct":"c","sol":"Literacy percentage of females\nNumber of females =327000-224000=103000.\nLiterate people

= 65 %

of 327000=212550.\nLiterate males

= 65 %

of 224000=145600.\nLiterate females =212550-145600=66950.\n $\"figure\"/$ \nRequired percentage

= \frac{66950}{103000} \times 100 = 65 %

.\nThe male rate is already equal to the overall rate, so the female rate has to match it as well - a quick way to spot the answer.\nHence the correct option is (c).","solHi":"महिला साक्षरता प्रतिशत\nमहिलाओं की संख्या =327000-224000=103000।\nसाक्षर व्यक्ति =327000 का

65 % = 212550

।\nसाक्षर पुरुष =224000 का

65 % = 145600

।\nसाक्षर महिलाएँ =212550-145600=66950।\n $\"figure\"/$ \nअभीष्ट प्रतिशत

= \frac{66950}{103000} \times 100 = 65 %

।\nपुरुषों की दर पहले से ही कुल दर के बराबर है, अतः महिलाओं की दर भी उतनी ही होनी चाहिए - उत्तर पहचानने का यह त्वरित तरीका है।\nइसलिए सही विकल्प (c) है।","pos":2,"neg":0.25},{"id":4558,"n":58,"subject":"Elementary Mathematics","stem":"Two trains having lengths of 210 m and 440 m are running at speeds of 60

km / h

and

90 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":"210 m और 440 m लंबाई वाली दो रेलगाड़ियाँ क्रमशः 60

km / h

और

90 km / h

की चाल से एक ही दिशा में चल रही हैं। पीछे से आती हुई तेज़ रेलगाड़ी द्वारा दूसरी रेलगाड़ी को पूरी तरह पार करने में लिया गया समय (मिनट में) है:","context":null,"contextHi":null,"options":[{"key":"a","text":"1.3","textHi":null,"imageUrl":null},{"key":"b","text":"2.2","textHi":null,"imageUrl":null},{"key":"c","text":"3","textHi":null,"imageUrl":null},{"key":"d","text":"1.9","textHi":null,"imageUrl":null}],"correct":"a","sol":"$2f","solHi":"$30","pos":2,"neg":0.25},{"id":4559,"n":59,"subject":"Elementary Mathematics","stem":"A sum of ₹ x amounts to ₹ 75867 in

2 \frac{1}{2}

years at

12 %

p.a., interest compounded after every 10 months. What is the value of

x

?","stemHi":"₹ x की एक राशि

2 \frac{1}{2}

वर्षों में

12 %

वार्षिक की दर से, प्रत्येक 10 महीने बाद ब्याज संयोजित होने पर, ₹ 75867 हो जाती है।

x

का मान क्या है?","context":null,"contextHi":null,"options":[{"key":"a","text":"56000","textHi":null,"imageUrl":null},{"key":"b","text":"58000","textHi":null,"imageUrl":null},{"key":"c","text":"55000","textHi":null,"imageUrl":null},{"key":"d","text":"57000","textHi":null,"imageUrl":null}],"correct":"d","sol":"$31","solHi":"$32","pos":2,"neg":0.25},{"id":4560,"n":60,"subject":"Elementary Mathematics","stem":"Gopal invests a sum of ₹5400 and Akshay invests a sum of ₹9400 at the same rate of simple interest per annum. If, at the end of 6 years, Akshay gets ₹720 more interest than Gopal, then find the rate of interest per annum (in percentage).","stemHi":"गोपाल ₹5400 की राशि तथा अक्षय ₹9400 की राशि समान वार्षिक साधारण ब्याज दर पर निवेश करते हैं। यदि 6 वर्ष के अंत में अक्षय को गोपाल से ₹720 अधिक ब्याज मिलता है, तो वार्षिक ब्याज दर (प्रतिशत में) ज्ञात कीजिए।","context":null,"contextHi":null,"options":[{"key":"a","text":"5","textHi":null,"imageUrl":null},{"key":"b","text":"2","textHi":null,"imageUrl":null},{"key":"c","text":"3","textHi":null,"imageUrl":null},{"key":"d","text":"4","textHi":null,"imageUrl":null}],"correct":"c","sol":"Simple interest from a difference\nIn simple interest,

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

, and here R and T are the same for both men.\nSo the extra interest comes only from the extra principal: 9400-5400=4000.\n

\frac{4000 \times R \times 6}{100} = 720

\n240R=720\n

R = \frac{720}{240} = 3

\nHence the rate of interest is 3% per annum, option (c).","solHi":"अंतर से साधारण ब्याज\nसाधारण ब्याज में

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

, और यहाँ दोनों के लिए R तथा T समान हैं।\nअतः अतिरिक्त ब्याज केवल अतिरिक्त मूलधन से आता है: 9400-5400=4000।\n

\frac{4000 \times R \times 6}{100} = 720

\n240R=720\n

R = \frac{720}{240} = 3

\nअतः वार्षिक ब्याज दर 3% है, विकल्प (c)।","pos":2,"neg":0.25}],"test":{"slug":"ssc-gd-constable--25-feb-2025-shift-1-maths","title":"SSC GD Constable 25 February 2025 Shift-1 — Elementary Mathematics Sectional Test","examName":"SSC GD","paperLabel":"25 February 2025 · Shift 1","sectionSubject":"Elementary Mathematics","durationMinutes":15,"format":"sectional_test"}}]