1. 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?

1. 4

2. 5

3. 6

4. 7

Answer & Explanation

Answer:- 3

Explanation :-

Let P completes the work in x days

Therefore, Q completes the work in x/2 days & R completes the work in x/3 days

P’s 1 day work = 1/x

Q’s 1 day work = 1/(x/2) = 2/x

R’s 1 day work = 1/(x/3) = 3/x

(P+Q+R)’s 1 day work = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x

6/x = 2 , x = 12

Time taken by Q to complete the work = 12/2 = 6 days

2. 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.

1. 12

2. 16

3. 20

4. 24

Answer & Explanation

Answer:- 1

Explanation :-

P’s 1 day Work = 1/15

Q’s 1 day Work = 1/10

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

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

Remaining work = 1 – 1/3 = 2/3

P completes the remaining work in = (2/3) / (1/15) = 10 days

Total time = 2 + 10 = 12 days

3. 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?

1. 10

2. 15

3. 18

4. 22

Answer & Explanation

Answer:- 3

Explanation :-

(P + Q)’s 1 day work = 1/30 ———-(1)

(Q + R)’s 1 day work = 1/24 ———-(2)

(P + R)’s 1 day work = 1/20 ———-(3)

By additing equation (1) ,(2) & (3)

2(P+Q+R)’s 1 day work = (1/30) + (1/24) + (1/20) = 1/8

(P+Q+R)’s 1 day work = (1/8)/2 = 1/16

(P+Q+R)’s 10 day work = 10/16 = 5/8

Remaining work = 1 – (5/8) = 3/8

P’s 1 day work = (1/16)- (1/24) = 1/48 P completes the remaining work in = (3/8) / (1/48) = 18 days

P completes the remaining work in = (3/8) / (1/48) = 18 days

4. P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in — days

1. 1

2. 2

3. 3

4. 4

Answer & Explanation

Answer:- 4

Explanation :-

Q completes the work in 12 days , Therefore P competes it in 6 days

P’s 1 day work = 1/6 & Q’s 1 day work = 1/12

1 day work of P & Q together = (1/6) + (1/12) = 3/12 = 1/4

Therefore , P & Q together completes the work in 4 days

5. A work can be finished in 16 days by 20 women. The same work can be finished in 15 days by 16 men. The ratio between the capacity of a man and a woman is

1. 1:3

2. 4:3

3. 2:3

4. 2:1

Answer & Explanation

Answer:- 2

Explanation :-

20 women completes the work in 16 days

1 woman completes the work in 16*20 days

Woman’s 1 day work = 1/(16*20)

15 men completes the work in 16 days

1 man completes the work in 15*16 days

Man’s 1 day work = 1/(15*16)

Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20 = 1/3 :1/4 = 4:3