Time and Work

1. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A. 8/15	B. 7/15
C. 11/15	D. 2/11

Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15

2. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
A. 9(3/5) days	B. 9(1/5) days
C. 9(2/5) days	D. 10 days

Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/16

Amount of work Q can do in 1 day = 1/12

Amount of work P, Q and R can together do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence R can do the job on 48/5 days = 9 (3/5) days

3. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
A. 10 days	B. 14 days
C. 15 days	D. 9 days

Answer : Option C

Explanation :

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days

4. A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together.
A. 18 days	B. 22 ½ days
C. 24 days	D. 26 days

Answer : Option B

Explanation :

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 22 ½ days

5. A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
A. Rs. 380	B. Rs. 600
C. Rs. 420	D. Rs. 400

Answer : Option D

Explanation :

Amount of work A can do in 1 day = 1/6

Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day

= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400