Time and Work with Explanation

Q22. Q can finish a work in 20 days while P in 15 days. If the work together 4 days, then find the fraction work that is left?

A.	B.
C.	D.

Answer- Option C

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 days' work =

7 60

* 4

=

7 15

Remaining work =

1 -

7 15

=

8 15

Q23. Nikki is 25% more efficient than Tina. Tina alone can build a craft in 20 days. Find the number of days taken by Nikki to finish the same piece of work?

Answer- Option D

Explanation-

Ratio of times taken by Tina and Nikki = 125 : 100 = 5 : 4.
Suppose Nikki takes x days to do the work.
5 : 4 :: 20 : x
x =

4 * 20 5

= 16 days.

Hence, Nikki takes 16 days to complete the work.

Q24. Worker P is 50% as efficient as worker Q. Worker R does half of the work done by P and Q together. If R alone does the work in 40 days, then P, Q, and R together can do the work in?

A. 20 days	B. 25 days
C. 13 days	D. 15 days

Answer- Option C

Explanation-

(Worker P's 1 day's work) : (Worker Q's 1 day's work) = 150 : 100 = 3 : 2.
Let P's and Q's 1 day's work be 3x and 2x respectively.
Then, Worker R's 1 day's work =

3x + 2x 2

=

5x 2

5x 2

=

1 40

or x =

1 40

x

2 5

=

1 100

P's 1 day's work =

3 100

;

Q's 1 day's work =

1 50

;

And, R's 1 day's work =

1 40

.

(P + Q + R)'s 1 day's work =

3 100

+

1 50

+

1 40

=

3 40

So, P, Q, and R together can do the work in

40 3

= 13

1 3

days.

Q25. A machine A can produce one thousand cars in 8 hours, machine B can produce the same numbers of cars in 10 hours, and machine C can produce them in 12 hours. All the machines started at 9 AM, but machine A is closed at 11 AM, and the remaining machines complete the work. Find the time at which the work will be completed?

Answer- Option A

Explanation-

(A + B + C)'s 1 hour's work =

1 8

+

1 10

+

1 12

=

37 120

Work done by A, B and C in 2 hours =

37 120

x 2

=

37 60

Remaining work =

1 -

37 60

=

23 60

(B + C)'s 1 hour's work =

1 10

+

1 12

=

11 60

Now,

11 60

work is done by B and C in 1 hour.
So,

23 60

work will be done by B and C in

60 11

x

23 60

=

23 11

hours ≈ 2 hours.

So, the work be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m.