Chain Rule Practice Problems: Level 01

1. 3600 men had provisions for 59 days. They started consuming, but after 10 days, reinforcement arrives. As a result, the remaining food lasted for 36 days. What was the strength of the reinforcement?
   1. 1300

   2. 1400
   3. 1500

   4. None of these

   Answer : Option 1
   3600 × 59 = (3600 × 10) + [(3600 + R)] × 36 ⇒ R = 1300

2. If either 24 men or 36 women can reap a field in 40 days, then 16 men and 16 women will reap the field in
   1. 36 days

   2. 16 days
   3. 9 days

   4. 8 days

    

   Answer : Option 1
   24 men = 36 women, 16men = 24 women. Since, 36 women can reap a field in 40 days.
   Therefore, (24+16) = 40 women can reap in (36 × 40)/40 = 36 days

3. 26 men complete a piece of work in 24 days working 9 hours a day. In how many days will 36 men complete the work working 6 hours a day?
   1. 27 days

   2. 30 days

   3. 26 days

   4. None of these

   Answer : Option 3
   We have: M₁ = 26, D₁ = 24, t₁ = 9, W₁ =1
   M₂ = 36, D₂ = ? , t₂ = 6, W₂=1 ∴ M₁D₁t₁W₂ = M₂D₂t₂W₁. So,26×24×9×1 = 36 × D₂× 6 × 1
   ⇒ D₂ = 26 days.

4.  38 persons can repair a road in 15 days, working 7 hours a day. In how many days will 35 persons, working 6 hours a day, complete the work?
   1. 9 days

   2. 13 days
   3. 17 days

   4. 19 days
   Answer : Option 4
   Let the required number of days be x. Now, applying the chain rule, we get 38 × 7 × 15 = 35 × 6 × x ⇒ x = (38 × 7 × 15) / (35 × 6 )⇒ = x = 19
5. If 9 binders bind 450 books in 15 days, how many binders will be required to bind 200 books in 10 days?
   1. 5

   2. 8
   3. 6

   4. 7

   Answer : Option 3
   Let the required number of binders be x.
   Less books, less binders (Direct Proportion)
   More days, less binders (Indirect Proportion)
   Books 450 : 200 : : 9 : x
   Days 15:10 ∴ (450 × 10 × x) = (200 × 15 × 9) ⇒ x = (200 × 15 × 9) / 450 × 10 = 6
6. 3 men and 6 boys can do a piece of work in 12 days; 4 men and 7 boys can do the same in 10 days. Then, 6 men and 6 boys can do three times the amount of this work in:
   1. 18 days

   2. 21 days
   3. 24 days

   4. 30 days

   Answer : Option 4
   (3 × 12) men + (6 × 12) boys = (4 × 10) men + (7 × 10) boys.⇒ 1boy = 2 men.
   ∴ (3men +6 boys) = (3+6×2) men = 15 men, (6 men + 6 boys) = (6 + 6 × 2)men = 18 men.
   Let the required number of days be x.
   Now, More men, less days (Indirect Proportion)
   More work, More days ( Direct Proportion)
   Men 18 : 15
   Work = 1:3 ∴ (18 × 1×x) = (15×3×12) ∴ x = 540/18 =30.
   Hence, the required number of days = 30

    

7. 40 labourers, working 8 hours a day can finish a piece of work in 21 days. If the labourers work 7 hours a day, then the number of labourers to finish the same piece of work in 40 days, will be:
   1. 15

   2. 21
   3. 24

   4. 25

   Answer : Option 3
   Let the required number for labourers be x. Then, lesser the working hrs / day, More are the labourers.
   i.e. More days, less labourers (Indirect Proportion )
   Working Hrs = 7:8
   Working Days = 40:21
   =7 × 40 : 8 × 21 :: 40 : x
   7 × 40 × x = 8 × 21 × 40
   ⇒ 7x = 168
   ⇒ x = 24

    

8. If 1200 men working for 6 hrs/day can check 4000 answer sheets in 20 days, then 3500 men working for 9hrs/day can check 7000 answer sheets in how many days?
   1. 8.5 days

   2. 8 days
   3. 9 days

   4. None of these

   Answer : Option 2
   D = 20 × (1200/3500) × (6/9) × (7000/4000) = 8 days

    

9. A certain number of men can finish a piece of work in 200 days. If, there were 20 men less, it would take 20 days more for the work to be finished. How many men were there originally?
   1. 50

   2. 100
   3. 200

   4. 220

   Answer : Option 4
   Original, let there be x men. Less men, More days ( Indirect Proportion ) ∴( x – 20 ) : x :: 200 : 220 ⇒ ( x – 20 ) ×220 = x × 200 ⇒ 20x = 4400 ⇒ x = 220.

    

10. In a diary farm, 30 cows eat 30 bags of husk in 50 days. In how many days will one cow eat one bag of husk?
    1. 12.5 days

    2. 25 days

    3. 50 days

    4. 100 days

    Answer : Option 3
    Let the required number of days be x.
    Less cows, More days ( Indirect Proportion )
    Less bags, Less days ( Direct Proportion )
    Cows : 1 : 30
    Bags : 30 : 1
    ∴ 1 × 30 × x = 30 × 1 × 50 ⇒ x = 50.

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