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AP ICET 2016 Paper

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Question : 107 of 200

Marks: +1, -0

A person A having completed 60% of the work in 15 days, calls another person B and they together finish the remaining work in 5 days. Then how many days B alone would have taken to do the whole work?

25
20
$37\,\frac{1}{2}$
37

Solution:

60% work ≡ 15 days

∴ 100% work

\equiv \frac{15 \times 100}{60} = 25

days

⇒ A alone can do the work in 25 days

Remaining work = 40%

= \frac{2}{5}

Let B alone do the work in x days.

\Rightarrow 5\left(\frac{1}{25}+\frac{1}{x}\right)=\frac{2}{5} \Rightarrow \frac{1}{x}=\frac{2}{25}-\frac{1}{25}=\frac{1}{25} \Rightarrow x=25

days

Aliter

Remaining 40 % work is done by A + B in 5 days

∴ A + B will do 60% work in

\frac{5 \times 60}{40} = \frac{15}{2}

A alone does 60% work in 15 days

⇒ A and B are equally efficient

∴ Time taken by B or A alone to do 100% work

= \frac{15 \times 100}{60.} = 25

days

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