Time & Work (2)

1. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in – days.
1. 4 days
2. 6 days
3. 2 days
4. 8 days

Explanation :-

(6m + 8w) can do a piece of work in 10 days
Therefore ,(3m + 4w) can do a piece of work in 2*10 = 20 days
5*(3m + 4w) can do a piece of work in 20/5 day = 4 days
Therefore , (15m + 20w)  can do a piece of work in = 4 days

2. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in — hours.
1. 12 hours
2. 6 hours
3. 8 hours
4. 10 hours

Explanation :-

Work done by A in 1 hour = 1/4
Work done by B & C in 1 hour = 1/3
Work done by A & C in 1 hour = 1/2
Work done by A,B & C in 1 hour = (1/4)+(1/3) = 7/12
Work done by B in 1 hour = (7/12)–(1/2) = 1/12
Therefore , B alone can complete the work in 12 hour

3. P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
1. 30 days
2. 25 day
3. 20 days
4. 15 days

Explanation :-

Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R  together in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day .
Therefore ,
Work done by 2P in 1 day  = 6/50
Work done by P in 1 day = 3/50
Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = (3/50)– (1/50) = 2/50 = 1/25
So Q alone can do the work in 25 days

4. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
1. 37 ½ days
2. 22 days
3. 31 days
4. 22 days

Explanation :-

Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 —(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days

5. Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?

1. 3 pm
2. 2 pm
3. 1:00 pm
4. 11 am

Explanation :-

Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P, Q and R together in 1 hour = (1/8) + (1/10) + (1/12) = 37/120
Work done by P, Q and R together work for 2 hours = 2 × (37/120) = 37/60
Remaining work = 1 – (37/60) = 23/60
When P stops working
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60Time taken by Q an R to complete the remaining work = (23/60) / (11/60) = 23/11
Time taken by Q an R to complete the remaining work = (23/60) / (11/60) = 23/11 ≈ 2 hours
Therefore , Time taken after 11 hours = 11+2 = 1:00 pm