Time and Work Solved problems

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 : 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, 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 : 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

3. 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 : 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

4. 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.A. 4 days
B. 6 days
C. 2 days
D. 8 days
Answer : A

Explanation :
Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = w
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8w = 1/10
=> 60m + 80w = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48w = ½
=> 52m + 96w = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and w = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days

5. P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5  days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?A. Rs.40
B. Rs.70
C. Rs.90
D. Rs.100
Answer : B

Explanation :
Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120     ---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130     ---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=>Amount Earned by R in 1 day = 70