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Time and Work ( 11 to 15 ):

# APTITUDE QUESTIONS (TIME AND WORK):

11. X and Y together can do a piece of work in 12 days, which Y and Z together can do in 16 days. After X has been working at it for 5 days and Y for 7 days, Z finishes it in 13 days. In how many days Z alone will do the work?

A) 24

B) 21

C) 26

D) 28

E) None of these

View Answer

Answer: option (A)

Explanation:

X’s 5 day’s work + Y’s 7 day’s work + Z’s 13 day’s work = 1

(X + Y)’s 5 day’s work + (Y + Z)’s 2 day’s work + Z’s 11 day’s work = 1

5/12 + 2/16 + Z’s 11 day’s work = 1

Z’s 11 day’s work = 1 – (5/12+ 2/16) = 11/24

Z’s 1 day’s work = (11/24* 1/11)= 1/24

∴ Z’s alone can finish the work in 24 days.

12. P can do a piece of work in 14 days which Q can do in 21 days. They started together but just 3 days before the completion of the work, P left. How many days are required to complete the work?

A) 6(3/5)

B) 8(1/2)

C) 10(1/5)

D) 13(1/2)

E) None of these

View Answer

Answer: option (C)

Explanation:

Q’s 3 days’ work = (1/21* 3)= 1/7. Remaining work = (1- 1/7)= 6/7

(P + Q)’s 1 day’s work = (1/14+ 1/21)= 5/42

Now, 5/42 work is done by P and Q in 1 day.

∴ 6/7 work is done by P and Q in (42/5* 6/7) = 36/5 days.

Hence, total time taken = (3+ 36/5) days = 10(1/5) days.

13. X, Y and Z together earn Rs. 300 per day, while P and R together earn Rs. 188 and Y and Z together earn Rs. 152. The daily earning of Z is:

A) Rs. 40

B) Rs. 68

C) Rs. 112

D) Rs. 150

E) None of these

View Answer

Answer: option (A)

Explanation:

Y’s daily earning = Rs. (300 – 188) = Rs. 112

X’s daily earning = Rs. (300 – 152) = Rs. 148

Z’s daily earning = Rs. [300 – (112 + 148) = Rs. 40

14. K can do a work in 3 days while D can do the same work in 2 days. If both of them finish the work together and get Rs. 150 then what is the share of K?

A) Rs. 30

B) Rs. 60

C) Rs. 70

D) Rs. 75

E) None of these

View Answer

Answer: option (B)

Explanation:

K’s wages : D’s wages = K’s 1 day’s work : D’s 1 day’s work = 1/3* 1/2 = 2:3

∴ K’s share = Rs. (2/5* 150)= Rs. 60

15. X alone can do a piece of work in 6 days and Y can alone in 8 days. X and Y undertook to do it for Rs. 3200. They completed the work in 3 days with the help of Z. How much is to be paid to Z?

A) Rs. 375

B) Rs. 400

C) Rs. 600

D) Rs. 800

E) None of these

View Answer

Answer: option (B)

Explanation:

Z’s day’s work = 1/3 – (1/6+ 1/8)= 1/3 – 7/24 = 1/24

X’s wages : Y’s wages : Z’s wages = 1/( 6) ∶ 1/8 ∶ 1/24 = 4:3:1

∴ Z’s share = Rs. (1/8* 3200)= Rs. 400