 # Time & Work (10)

1.A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in ?
1. 15 days
2. 10 days
3. 9 days
4. 8 days
5. None of these

Explanation :-

Lets suppose A can complete the work in x days
Therefore B can complete the work in 3x days
3x – x = 10
x = 5
B can complete the work in 3*5 = 15 days

2.4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?
1. 30 days
2. 40 days
3. 50 days
4. 60 days
5. None of these

Explanation :-

Lets suppose work done by 1 man in 1 day = x
and 1 woman’s 1 days work = y.
Then, 4x + 6y = 1/8 ——— Multiply it by 3
and 3x+7y = 1/10 ———–Multiply it by 4
we get ,
12x + 18x = 3/8
12x + 28x =4/10
By subtracting both the equations,
we get , y = 1/400
1 day work of 10 women = 10/400 = 1/40
Therefore , 10 women will finish the work in 40 days

3.10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
1. 6 days
2. 7 days
3. 8 days
4. 9 days
5. None of these

Explanation :-

10 women complete the work in 7 days
5 women complete the work in 7*2 = 14 days
10 children complete the work in = 14 days
One day work of 5 women & 10 children = (1/14) + (1/14) = 2/14 = 1/7
Therefore , They complete the work in 7 days

4. 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio?
1. 1:2
2. 1:3
3. 2:1
4. 2:3
5. None of these

Explanation :-

Lets suppose work done by 1 man in 1 day = x
work done by 1 boy in 1 day = y
Therefore , According to Question
5x + 2y = 4(x+y)
x = 2y => x/y = 2/1
Therefore , x : y = 2 : 1

5. A work is done by three person A,B and C. A alone takes 10 hours to complete a single product but B and C working together takes 4 hours, for the completion of the same product. If all of them worked together and completed 14 products, then how many hours have they worked?
1. 20 hrs
2. 28 hrs
3. 40 hrs
4. 54 hrs
5. None of these

Explanation :-

No. of products completed by Ain 1 Hour  (1/A) = 1/10
No. of products completed by (B+C) in 1 Hour = 1/4 (Given)
(1/A) + (1/B) + (1/C) =  (1/10) + (1/4) = 7/20
Therefore
In 20 hours, working together they will complete 7 products.
Thus in 40 hours they will complete 14 products

6. Adam can do a job in 15 days, John can do the same job in 20 days. If they work together for 4 days on this job. What fraction of job is incomplete ?
1. 1/4
2. 1/10
3. 7/15
4. 8/15
5. none of these