# Time and Work ( 6 to 10 )

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Time and Work ( 6 to 10 ):

# APTITUDE QUESTIONS (TIME AND WORK):

6. P is twice as good a workman as Q and together they finish a piece of work in 14 days. The number of days taken by P alone to finish the work is:

A) 31

B) 21

C) 24

D) 20

E) None of these

Explanation:

(P’s 1 day’s work) : (Q’s 1 day’s work) = 2:1
(P + Q)’s 1 day’s work = 1/14
Divide 1/14 in the ratio 2:1
∴ P’s 1 day’s work = (1/14*2/3)= 1/21
Hence, P alone can finish the work in 21 days.

7. S can do a piece of work in 20 days. T is 25% more efficient than S. How many days taken by T to do the same piece of work?

A) 17

B) 16

C) 15

D) 19

E) None of these

Explanation:

Ratio of times taken by S and T = 125:100 = 5:4
Suppose, T takes x days to do the work
5:4 :: 20: x => x = ((4 * 20)/5) => x = 16 days.
Hence, T takes 16 days to complete the work.

8. C is 50% efficient as D. E does half of the work done by C and D together. If E alone does the work in 40 days, then C, D and E together can do the work in:

A) 13(1/3) days

B) 15 days

C) 20 days

D) 30 days

E) None of these

Explanation:

(C’s day’s work): (D’s day’s work) = 150:100 = 3:2
Let C’s and D’s 2 day’s work be 3x and 2x respectively.
Then, E’s 1 day’s work = ((3x+ 2x)/2)= 5x/2
∴ 5x/2 = 1/40 or x = (1/40*2/5)= 1/100
C’s 1 day’s work = 3/100; D’s 1 day’s work = 1/50; E’s 1 day’s work = 1/40
(C + D + E)’s 1 day’s work = (3/100+ 1/50+ 1/40)= 15/200 = 3/40
So, C, D and E together can do the work in 40/3 = 13(1/3) days

9. P can do a work in 15 days and Q in 20 days. If P and Q work on it together for 4 days, then the fraction of the work that is left is:

A) 1/3

B) 1/20

C) 7/15

D) 8/15

E) None of these

Explanation:

P’s 1 day’s work = 1/15; Q’s 1 day’s work = 1/20
(P + Q)’s 1 day’s work = (1/15+ 1/20) = 7/60
(P + Q)’s 4 day’s work = (7/60*4)= 7/15
∴ Remaining work = (1- 7/15)= 8/15

10. P can finish a work in 24 days, Q in 9 days and R in 12 days. Q and R started the work together but left after 3 days. The remaining work was done by P in:

A) 5 days

B) 6 days

C) 10 days

D) 101/2 days

E) None of these

Explanation:

(Q + R)’s 1 day’s work = (1/9+ 1/12)= 7/36
Work done by Q and R in 3 days = (7/36*3)= 7/12
Remaining work = (1- 7/12)= 5/12
Now, 1/24 work is done by P in 1 day
So, 5/12 work is done by P in (24* 5/12)= 10 days