# Time & Work (9)

1. To Finish a work, B will take three times as long as A and C together and C will take twice as long as A and B together. If the three persons A, B and C together can finish the work in 20 days , then how long will A take to finish the work alone?
1. 30 days
2. 45 days
3. 48 days
4. 60 days
5. None of these

Explanation :-

Let time taken by A & C  to complete the Work = x days
Therefore , Time taken by B to complete the Work  = 3x days
Therefore , Work done by A, B and C in 1 day = (1/x) + (1/3x)
(1/x) + (1/3x) = 1/20
x = 80/3
Let time taken by A & B  to complete the Work = y days
Therefore , Time taken by C to complete the Work  = 2x days
Therefore , Work done by A, B and C in 1 day = (1/y) + (1/2y)
(1/y) + (1/3y) = 1/20
y = 30
Now ,
Work done by A, B and C in 1 day = (1/A) + (1/3x) + (1/2y) = 1/20
A = 48 days

2. Ram takes 6 hours to type 32 pages. Shaam takes 5 hours to type 40 pages. In how many hours they will type 110 pages together ?
1. 7 hours
2. 8 hours
3. 8 hours 15 min
4. 8 hours 30 mins7 hours
5. None of these

Explanation :-

Number of pages typed by Ravi in 1 hour = 32/6 = 16/3
Number of pages typed by Kumar in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour =(16/3) + 8 = 40/3
Time taken by both to type 110 pages =110 * (3/40) = 8 1⁄4

3.7 men take 12 days to complete a job. They worked for 5 days, after 5 days 2 men left the job. In how many days 5 men will complete the job ?
1. 5 days
2. 7 days
3. 9 days
4.10 days
5. None of these

Explanation :-

7 Man can complete the work in 12 days
5 days work of 7 men = 5/12
Remaining Work = 1 – (5/12) = 7/12
1 man can complete the work in = 12*7 = 84
1 day work of a man = 1/84
5 day work of  men = 5/84
Time taken by 5 men to complete the Remainning work = (7/12)/(5/84) = 49/5 days

4.If A, B and C can do a job in 20, 30 and 60 days respectively. In how many days A can do the work if B and C help him on every third day ?
1. 12 days
2. 15 days
3. 16 days
4. 18 days
5. None of these

Explanation :-

Work done by A in 1 day = 1/20
Work done by B in 1 day = 1/30
Work done by C in 1 day = 1/60
Work done by A in 2 days = 2/20 = 1/10
Work done by A ,B & C in every third day = (1/20) + (1/30 + (1/60) = 1/10
Work completed in every 3 days = (1/10) + (1/10) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days

5.A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work?
1. 27 days
2. 54 days
3. 56 days
4. 68 days
5. None of these