15. P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in --- days if all of them are working together.

A. 2 B. 3 ³⁄₇ C. 4 ¼ D. 5

**Answer : Option B**

Explanation : Work done by P in 1 day = 1/24

Work done by Q in 1 day = 1/6

Work done by R in 1 day = 1/12

Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24

=> Working together, they will complete the work in 24/7 days = 3 ³⁄₇days

16. 10 men can complete a work in 7 days. But 10 women7 need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?

A. 5 B. 6 C. 7 D. 8

**Answer : Option C**

Explanation :Work done by 10 men in 1 day = 1/7

Work done by 1 man in 1 day = (1/7)/10 = 1/70

Work done by 10 women in 1 day = 1/14

Work done by 1 woman in 1 day = 1/140

Work done by 5 men and 10 women in 1 day = 5 × (1/ 70) + 10 × (1/140)

= 5/70 + 10/140 = 1/7

=> 5 men and 10 women can complete the work in 7 days

17. Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in ----- days.

A.14 B. 16 C. 18 D. 20

**Answer : Option B**

Explanation :Work done by Kamal in 1 day = 1/20

Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16

=> Suresh can complete the work in 16 days

18. P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?

A. 5 days B. 10 days C. 14 days D. 22 days

**Answer : Option B**

Explanation : Work done by P in 1 day = 1/20

Work done by Q in 1 day = 1/12

Work done by P in 4 days = 4 × (1/20) = 1/5

Remaining work = 1 – 1/5 = 4/5

Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15

Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6

Total days = 4 + 6 = 10

19. P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?

A. 4 B. 5 C. 6 D. 7

**Answer : Option C**

Explanation :Let P takes x days to complete the work

Then Q takes x/2 days and R takes x/3 days to finish the work

Amount of work P does in 1 day = 1/x

Amount of work Q does in 1 day = 2/x

Amount of work R does in 1 day = 3/x

Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x

= 1/x (1 + 2 + 3) = 6/x

6/x = 2

=> x = 12

=> Q takes 12/2 days = 6 days to complete the work

20. P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.

A. 12 B. 16 C. 20 D. 24

**Answer : Option A**

Explanation : Work done by P in 1 day = 1/15

Work done by Q in 1 day = 1/10

Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6

Work done by P and Q in 2 days = 2 × (1/6) = 1/3

Remaining work = 1 – 1/3 = 2/3

Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days

Total time taken = 2 + 10 = 12 days

21. P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?

A. 10 B. 15 C. 18 D. 22

**Answer : Option C**

Explanation : Let work done by P in 1 day = p,

Work done by Q in 1 day = q,

Work done by R in 1 day = r

p + q = 1/30

q + r = 1/24

r + p = 1/20

Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20

= 15/120 = 1/8

=> p + q + r = 1/16

=> Work done by P,Q and R in 1 day = 1/16

Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8

Remaining work = 1 = 5/8 = 3/8

Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day

= 1/16 – 1/24 = 1/48

Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

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