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CAT 2018 [SLOT 2] Quant Question with Solution 16

Question:
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. 13.5
  2. 11
  3. 12
  4. 14.5
Show Answer
Correct Answer: 1
Let r and g be the rates of work of Ramesh and Ganesh respectively.
Let $(\mathrm{r}+\mathrm{g}) 16=1$
$\Rightarrow(r+g)=\frac{1}{16}$
$(r+g) 7=\frac{7}{16}$
Remaining work to be done $=\frac{9}{16}$
Given, $(0.7 r+g) 10=\frac{9}{16}$
$7 r+10 g=9 r+9 g$
$g=2 r$
$r=\frac{1}{48}$
$g=\frac{1}{24}$
Time taken by g alone to complete the work $=\frac{\frac{9}{16}}{\frac{1}{24}}$=13.5

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