**Chain Rule Practice Problems : Level 02**

**If 9 men or 12 women can do a piece of work in 30 days, in how many days, can the work be done by 6 men and 12 women working together?**1. 12 days2. 15 days3. 9 days4. 18 days5. 10 days**Answer :**Option 4

9M = 12W ⇒6M=8W

Hence, 6M + 12W = 8W + 12W = 20 W. Since 12W can do a piece of work in 30 days, so 20W can do the same work in (12 × 30)/20 = 18 days.**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. 18 days2. 12 days3. 16 days4. 36 days5. 9 days**Answer :**Option 4

Let the number of men originally = M. According to the given condition, 24M = 36W ⇒2M = 3W

16M + 16W = 24W + 16W = 40W. Since 36 women can reap a field in 40 days, so 40 women can reap the same field in ( 36 × 40)/40 = 36 days.**A garrison of 850 men has provisions for 30 weeks. If at the end of 10 weeks, they are re-inforced by 850 men, how long will the provisions last?**1. 8 weeks2. 12 weeks3. 14 weeks4. 15 weeks5. 10 weeks**Answer :**Option 5

850 × 30 = 850 × 10 + 1700 × W ⇒ W = 10 weeks**If 7 men can reap 70 hectares in 35 days, how many hectares can 34 men reap the same field in 21 days?**1. 102 hectares2. 204 hectares3. 408 hectares4. 816 hectares5. None of these**Answer :**Option 2

H=70 × (34/7) × (21/35) = 204 hectares**If 25 men working 9 hours a day can do a piece of work in 24 days, in how many days will 18 men working 8 hours a day do the same work ?**1. 20 1/2 days2. 22 1/2 days3. 37 1/2 days4. 25 days5. None of these**Answer :**Option 3

D=24 × (25/18) × (9/8) = 37(1/2)days

**If 18 men working 15 hours a day can do a piece of work in 36 days, in how many days will 27 men working 9 hours a day do the same work ?**1. 40 days2. 30 days3. 20 days4. 10 days5. None of these**Answer :**Option 1

D=36 × (15/9) × (18/27) = 40days**5 men or 2 women can do a piece of work in 34 days. Then 1 men and 3 women will do a piece of work thrice as large in:**1. 30 days2. 25 days3. 27 days4. 60 days5. 21 days**Answer :**Option 4

Now, 5M = 2W ⇒ 1W = (5/2) M ⇒ 3W = 15/2M

Total persons = 1M + 3W = 1M + 15/2M = 17/2M

Therefore, no. of days = 5 × (34/17) × 3 × 2 = 60 days.**If 16 men can dig a trench 150 m long, 2 m wide and 3 m deep in 4 days of 15 hours each, in how many days of 7 hours each will 15 men dig trench 100 m long, 3 m wide and 3 m deep?**1. 11 ½ days2. 9(1/7)days3. 7(1/9)days4. 10 days5. None of these**Answer**: Option 2

Volume of trench dug before= 150 × 2 × 3 = 900 and new volume= 100 × 3 × 3 = 900. As both are same, it is not going to make any difference. So, new days= 4 × (16/15) × (15/17) = 9(1/7) days**A M.E.S contractor undertake to renew the floor of a building within 40 days and immediately employ 27 men upon it. At the end of 31 days the work is only half done. How many more men should he employ to complete the work in time?**1. 26 men2. 36 men3. 46 men4. 56 men5. 66 men**Answer :**Option 5

Days left are (40 – 31) = 9. By chain rule, total no. of men required = 27 × (31/9) = 93, therefore additional men required = 93 – 27 =66 men**Five men and three boys can do a piece of work in 15 days while 7 men and 8 boys can do the same work in 8 days. How long will 12 men and 8 boys take to do it?**1. 5 days2. 7 days3. 6 days4. 8 days5. None of these**Answer :**Option 3

(5M + 3B) × 15 = (7M + 8B) × 8

⇒ 75M + 45B = 56M + 64B

⇒ M = B

So 8 men can do a work in 15 days. Hence(12 + 8)

⇒ 20men can do the same work in 6 days