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Direction : Study the following questions carefully and choose the right answer.
1
A contractor hire Amitabh Arora to complete the work and Amitabh can do the work in 25 days. Amitabh worked for 5 days and after that Bindu singh completed it in 20 days. In how many days will Amitabh and Bindu together finish the work?
» Explain it
A
Amitabh can do a piece of work in 25 days.

In 5 days he can do 1/5th work.

Rest work = 1 –  1  =  4
5 5

Bindu can complete 4/5th of the work in 20 days so he can do the complete work in 25 days.
Amitabh's 1 day work =  1
25

Bindu's 1 day work =  1
25

(Amitabh and Bindu)'s 1 day work =  1  +  1  =  2
25 25 25

Amitabh and Bindu together can complete the work in =  25  days
2

Hence, option A is correct.
 
2
Arnab is twice as fast as Bhanu, and Bhanu is one-third as fast as Chandu. If together they can complete work in 30 days, in how many days can Arnab, Bhanu and Chandu do the work respectively?
» Explain it
C
Let's Chandu can do the work in 2x days.

Bhanu can do it in 6x days and Arnab can do it in 3x days.

1  +  1  +  1  =  1  ⇒  3 + 1 + 2  =  1  ⇒ x = 30
2x 6x 3x 30 6x 30

So, the time taken to complete the work by Arnab, Bhanu and Chandu is 90, 180, 60 days respectively.

Hence, option C is correct.
 
3
Vijay can do a piece of work in 24  days. Rakesh can do the same work in 30 days and Vinod in 40 days. Vijay and Vinod worked for 4 days and handed it to Rakesh. Rakesh worked for some days and handed it again to Vijay and Vinod 6 days before completing the work. For how many days did Rakesh work?
» Explain it
B
Combined work done by Vijay and Vinod in  4 + 6 days (4 initial days and last 6 days)

=     10  +  10  =  2
24 40 3

∴   Remaining work = 1 –  2  =  1
3 3

Rakesh works for  ( 1  × 30 )  =  10 days
3

Hence, option B is correct.

4
If three men and two women can do the same piece of work as two men and three women, then what is the ratio of efficiency of men and women?
» Explain it
C
Given, 

Work done by (3 M + 2 W) = Work done by (2 M + 3 W)

⇒ 3 M – 2 M = 3 W – 2 W

⇒ 1 M = 1 W

⇒ M : W = 1 : 1

Option C is hence the correct answer.
5
A can finish a work in 5 days and B takes 4 days to do the same work. If the work is increased by 8 times, How many days will it take for both of them to finish the work if they work together?
» Explain it
D
Let the total work be 100%

A can do the work in 5 days, so he can do 20% work in 1 day

B can do the work in 4 days, so he can do 25% work in 1 day

Together they can do 20+25 = 45% work in 1 day

Now the work is increased by 800%, so the work becomes 900%

The work can be done in  900  = 20 days
45

Hence, option D is correct.