Quantitative Aptitude

Chain Rule: Practice Questions with Answers

69 practice questions on Chain Rule, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.51

   11 labourers can build a wall 220 m long in 14 days. In how many days will 42 labourers build a wall 240 m long?

   1. A 3 days
   2. B 4 days
   3. C 5 days
   4. D 6 days
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   Correct answer: (B) 4 days

   Days vary inversely with the number of labourers (× 11/42) and directly with the length (× 240/220). Days = 14 × 11/42 × 240/220 = 4.

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2. Q.52

   12 machines can make 540 toys in 9 hours. How many toys can 10 machines make in 5 hours?

   1. A 810
   2. B 250
   3. C 360
   4. D 275
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   Correct answer: (B) 250

   Output varies directly with the number of machines and with the time. Output = 540 × 10/12 × 5/9 = 250.

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3. Q.53

   13 carpenters earn Rs 28,600 in 11 days. In how many days will 3 carpenters earn Rs 13,800 at the same daily rate?

   1. A 22 days
   2. B 25 days
   3. C 23 days
   4. D 24 days
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   Correct answer: (C) 23 days

   Days vary directly with the earnings and inversely with the number of carpenters. Days = 11 × 13,800/28,600 × 13/3 = 23.

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4. Q.54

   A hostel has enough rice for 440 students for 42 days at 500 g per student per day. If the number of students becomes 700 and each gets 300 g a day, how many days will the stock last?

   1. A 44 days
   2. B 55 days
   3. C 33 days
   4. D 66 days
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   Correct answer: (A) 44 days

   Days vary inversely with both the number of students and the daily ration. Days = 42 × 440/700 × 500/300 = 44.

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5. Q.55

   If 3 labourers earn Rs 21,600 in 12 days, how much will 19 labourers earn in 4 days at the same daily rate?

   1. A Rs 45,600
   2. B Rs 50,160
   3. C Rs 36,480
   4. D Rs 60,800
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   Correct answer: (A) Rs 45,600

   Earnings vary directly with the number of labourers and with the days. Earnings = 21,600 × 19/3 × 4/12 = Rs 45,600.

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6. Q.56

   14 labourers can harvest a field in 24 days. In how many days will 28 labourers harvest the same field?

   1. A 48 days
   2. B 38 days
   3. C 12 days
   4. D 10 days
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   Correct answer: (C) 12 days

   Men and days are inversely proportional for the same job. Days = 24 × 14/28 = 12.

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7. Q.57

   30 labourers can build a wall in 10 days. How many labourers are needed to build the same wall in 25 days?

   1. A 45
   2. B 12
   3. C 15
   4. D 16
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   Correct answer: (B) 12

   For the same job, the number of labourers is inversely proportional to the days. Labourers = 30 × 10/25 = 12.

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8. Q.58

   35 workers working 6 hours a day can dig a canal in 24 days. How many hours a day must 20 workers work to dig the same canal in 21 days?

   1. A 16 hours
   2. B 3 hours
   3. C 8 hours
   4. D 12 hours
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   Correct answer: (D) 12 hours

   Hours a day vary inversely with both the number of workers and the days. Hours = 6 × 35/20 × 24/21 = 12.

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9. Q.59

   20 men working 8 hours a day can complete a piece of work in 21 days. How many hours a day must 40 men work to complete the same work in 14 days?

   1. A 4 hours
   2. B 8 hours
   3. C 9 hours
   4. D 6 hours
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   Correct answer: (D) 6 hours

   Hours a day vary inversely with both the number of men and the days. Hours = 8 × 20/40 × 21/14 = 6.

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10. Q.60

    33 men working 10 hours a day can dig a canal 150 m long in 27 days. How many men working 12 hours a day are needed to dig a canal 140 m long in 7 days?

    1. A 132
    2. B 100
    3. C 99
    4. D 66
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    Correct answer: (C) 99

    Men are inverse to hours a day (× 10/12) and to days (× 27/7), direct to length (× 140/150). Men = 33 × 10/12 × 27/7 × 140/150 = 99.

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11. Q.61

    33 men working 8 hours a day can dig a canal 240 m long in 21 days. In how many days will 12 men working 7 hours a day dig a canal 200 m long?

    1. A 66 days
    2. B 44 days
    3. C 56 days
    4. D 55 days
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    Correct answer: (D) 55 days

    Days are inverse to men (× 33/12) and to hours a day (× 8/7), direct to length (× 200/240). Days = 21 × 33/12 × 8/7 × 200/240 = 55.

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12. Q.62

    A relief camp has rations for 700 people for 36 days. After 12 days, 350 more people join. For how many more days will the remaining food last?

    1. A 16 days
    2. B 48 days
    3. C 24 days
    4. D 12 days
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    Correct answer: (A) 16 days

    Food left after 12 days = food for 700 people for 24 days. Now there are 1,050 people, so days = 700 × 24/1,050 = 16.

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13. Q.63

    33 labourers can harvest a field in 10 days. How many labourers are needed to harvest the same field in 11 days?

    1. A 30
    2. B 20
    3. C 34
    4. D 32
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    Correct answer: (A) 30

    For the same job, the number of labourers is inversely proportional to the days. Labourers = 33 × 10/11 = 30.

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14. Q.64

    22 men working 6 hours a day can paint a building in 15 days. In how many days will 11 men working 9 hours a day paint the same building?

    1. A 45 days
    2. B 24 days
    3. C 20 days
    4. D 5 days
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    Correct answer: (C) 20 days

    More men or more hours a day both mean fewer days (inverse). Days = 15 × 22/11 × 6/9 = 20.

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15. Q.65

    A garrison of 1,000 men has food for 34 days. After 20 days, 440 men leave. For how many more days will the remaining food last?

    1. A 25 days
    2. B 20 days
    3. C 14 days
    4. D 30 days
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    Correct answer: (A) 25 days

    Food left after 20 days = food for 1,000 men for 14 days. Now there are 560 men, so days = 1,000 × 14/560 = 25.

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16. Q.66

    A ship has provisions for 150 passengers for 78 days. After 30 days, 50 more passengers join. For how many more days will the remaining food last?

    1. A 72 days
    2. B 36 days
    3. C 27 days
    4. D 48 days
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    Correct answer: (B) 36 days

    Food left after 30 days = food for 150 passengers for 48 days. Now there are 200 passengers, so days = 150 × 48/200 = 36.

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17. Q.67

    14 labourers can build a wall in 30 days. In how many days will 15 labourers build the same wall?

    1. A 42 days
    2. B 29 days
    3. C 28 days
    4. D 31 days
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    Correct answer: (C) 28 days

    Men and days are inversely proportional for the same job. Days = 30 × 14/15 = 28.

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18. Q.68

    9 painters earn Rs 13,500 in 10 days. In how many days will 15 painters earn Rs 54,000 at the same daily rate?

    1. A 24 days
    2. B 16 days
    3. C 36 days
    4. D 18 days
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    Correct answer: (A) 24 days

    Days vary directly with the earnings and inversely with the number of painters. Days = 10 × 54,000/13,500 × 9/15 = 24.

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19. Q.69

    A hostel has enough rice for 60 students for 55 days at 700 g per student per day. If the number of students becomes 140 and each gets 550 g a day, how many days will the stock last?

    1. A 30 days
    2. B 27 days
    3. C 20 days
    4. D 24 days
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    Correct answer: (A) 30 days

    Days vary inversely with both the number of students and the daily ration. Days = 55 × 60/140 × 700/550 = 30.

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