**Chain Rule Practice Problems: Level 01**

**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. 13002. 14003. 15004. None of these**Answer :**Option 1

3600 × 59 = (3600 × 10) + [(3600 + R)] × 36 ⇒ R = 1300**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 days2. 16 days3. 9 days4. 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**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 days2. 30 days3. 26 days4. None of these**Answer :**Option 3

We have: M_{1}= 26, D_{1}= 24, t_{1}= 9, W_{1}=1

M_{2}= 36, D_{2}= ? , t_{2}= 6, W_{2}=1 ∴ M_{1}D_{1}t_{1}W_{2}= M_{2}D_{2}t_{2}W_{1}. So,26×24×9×1 = 36 × D_{2}× 6 × 1

⇒ D_{2}= 26 days.-
**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 days2. 13 days3. 17 days4. 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 **If 9 binders bind 450 books in 15 days, how many binders will be required to bind 200 books in 10 days?**1. 52. 83. 64. 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**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 days2. 21 days3. 24 days4. 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**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. 152. 213. 244. 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**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 days2. 8 days3. 9 days4. None of these**Answer**: Option 2

D = 20 × (1200/3500) × (6/9) × (7000/4000) = 8 days**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. 502. 1003. 2004. 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.**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 days2. 25 days3. 50 days4. 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.