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Time required for Ganesh to complete work alone

CAT 2018 Slot 2 · Quantitative Ability · Medium · Time & Work

This is a medium Quantitative Ability question from the CAT 2018 Slot 2 paper. It tests Time & Work. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would he have completed the remaining work?

  1. A.

    12

  2. B.

    14.5

  3. C.

    13.5

  4. D.

    11

Answer

C

Explanation

Let daily work of Ramesh be RR and Ganesh be GG. Total work =16(R+G)= 16(R + G).

Work remaining after 7 days =9(R+G)= 9(R + G). For the next 10 days (total 17 days), Ramesh works at 0.7R0.7R and Ganesh at GG. So: 10(0.7R+G)=9(R+G)10(0.7R + G) = 9(R + G) 7R+10G=9R+9G  ⟹  2R=G  ⟹  G=2R7R + 10G = 9R + 9G \implies 2R = G \implies G = 2R

Work remaining after 7 days =9(R+2R)=27R= 9(R + 2R) = 27R.

If Ganesh works alone after Ramesh gets sick, time taken by Ganesh =27RG=27R2R=13.5 days= \frac{27R}{G} = \frac{27R}{2R} = 13.5\text{ days}.

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