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Anushka and Anirudh working together can complete a piece of work in 20 days. They started the work together, but Anushka left after x days and Anirudh finished the remaining work in the next x/2 days. Had Anushka left after 3x/4 days, Anirudh would have taken x days to finish the remaining work. Find the ratio of the efficiency of Anushka to that of Anirudh.
(2013)
  • a)
    2 : 3
  • b)
    3 : 2
  • c)
    2 : 1
  • d)
    1 : 1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Anushka and Anirudh working together can complete a piece of work in 2...
Let the efficiencies of Anirudh and Anushka be 'a' and 'b' units/day respectively.
according to question,

So, the required ratio is 1 : 1.
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Anushka and Anirudh working together can complete a piece of work in 2...
Given: Anushka and Anirudh working together can complete a piece of work in 20 days.

Let the total work be W.

Let the efficiency of Anushka be A and that of Anirudh be B.

Then, A + B = W/20 ------(1)

Anushka worked for x days and then left. So, the remaining work done by Anirudh in x/2 days is (1 - x/20)W.

Anirudh's efficiency is B. So, B(x/2) = (1 - x/20)W

=> B = (1 - x/20)W/(x/2) ------(2)

Had Anushka left after 3x/4 days, then she worked for (3x/4) days and the remaining work done by Anirudh in x/4 days is (1 - 3x/80)W.

Anirudh took x days to finish the remaining work. So, B(x/4) = (1 - 3x/80)W

=> B = (1 - 3x/80)W/(x/4) ------(3)

Equating (2) and (3), we get:

(1 - x/20)W/(x/2) = (1 - 3x/80)W/(x/4)

Simplifying, we get:

x = 10

Substituting x = 10 in (1), we get:

A + B = W/20

=> A + 2B = W/10

=> A/B = 1/2

Therefore, the ratio of the efficiency of Anushka to that of Anirudh is 1:2, which is option (d).
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Community Answer
Anushka and Anirudh working together can complete a piece of work in 2...
Let the efficiencies of Anirudh and Anushka be 'a' and 'b' units/day respectively.
according to question,

So, the required ratio is 1 : 1.
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Anushka and Anirudh working together can complete a piece of work in 20 days. They started the work together, but Anushkaleft after x days and Anirudh finished the remaining work in the next x/2 days. Had Anushka left after 3x/4 days, Anirudh wouldhave taken x days to finish the remaining work. Find the ratio of the efficiency of Anushka to that of Anirudh.(2013)a)2 : 3b)3 : 2c)2 : 1d)1 : 1Correct answer is option 'D'. Can you explain this answer?
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