 # Time & Work (4)

1. P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in — days if all of them are working together.
1. 2
2. 3 3⁄7
3. 4 ¼
4. 5

Explanation :-

P’s 1 day work = 1/24,   Q’s 1 day work = 1/6    R’s 1 day work = 1/12
(P+Q+R)’s 1 day work = (1/24) + (1/6) +  (1/12) = 7/24
Whole work can be completed by P,Q & R together in 24/7 days or in (3 and  3/7) days

2. 10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
1. 5
2. 6
3. 7
4. 8

Explanation :-

10 men can complete a work in 7 days
5 man can complete the work in 7*2 = 14 days
10 women can complete a work in 14 days
1 day work of (5 men & 10 women) together  = (1/14) + (1/14) =1/7
Therefore, 5 men & 10 women together can complete the work in 7 days

3. Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in — days.
1. 14
2. 16
3. 18
4. 20

Explanation :-

Kamal’s 1 day work = 1/20
Suresh’s 1 day work = (1/20) × (125/100) = 5/80 = 1/16
Therefore, Suresh can complete the work in 16 days

4. Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
1. 7 hour 15 minutes
2. 7 hour 30 minutes
3. 8 hour 15 minutes
4. 8 hour 30 minutes

Explanation :-

Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil & Suresh together in 1 hour = 16/3 + 8 = 40/3
Time taken By Anil & Suresh together  to type 110 pages = 110 × 3 /40 = 33/4
=> 8 ¼ hours
=> 8 hour 15 minutes

5. P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
1. 5 days
2. 10 days
3. 14 days
4. 22 days