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CAT 2018 Slot 2 — QA Question 6

Working in ShiftsEasy

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?

Answer & solution

  • A

    12

  • B

    11

  • 13.5

  • D

    14.5

Solution

Easy

Let Ramesh and Ganesh do RR and GG units of work per day. The total work can be written two ways — the planned 1616 days, and the actual 77 days full + 1010 days with Ramesh at 70%70\%. Equate them to find GG in terms of RR, then find how long Ganesh alone takes for the work left after day 7.

1

Two expressions for the same total work. Planned: 16(R+G)16(R+G). Actual: 7(R+G)7(R+G) at full rate plus 1010 days with Ramesh at 0.7R0.7R.

16(R+G)=7(R+G)+10(0.7R+G)⇒ 16R+16G=14R+17G⇒ G=2R\begin{aligned} &16(R+G) = 7(R+G) + 10(0.7R+G)\\ &\Rightarrow\ 16R+16G = 14R+17G\\ &\Rightarrow\ G = 2R \end{aligned}
2

Work remaining after day 7. Total =16(R+G)=16(R+G); the pair finishes 7(R+G)7(R+G) in the first 77 days, leaving 9(R+G)9(R+G).

Wleft=9(R+G)=9(R+2R)=27R(using G=2R)\begin{aligned} &W_{\text{left}} = 9(R+G) = 9(R+2R) = 27R \quad\text{(using }G=2R) \end{aligned}
3

Ganesh alone on the remainder. Ganesh's rate is G=2RG=2R.

t=27R2R⇒ t=13.5 days\begin{aligned} &t = \frac{27R}{2R}\\ &\Rightarrow\ t = 13.5\ \text{days} \end{aligned}
t=13.5 days(option c)t = 13.5\ \text{days}\quad\text{(option c)}
CAT 2018 Slot 2 QA Q6: Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got si — Solution | TheCATExam