A can do a work In 45 days. He works at it for 15 days and then, $B$ alone finishes the remaining work in 24 days. Find the time taken to complete $80 %$ of the work, if they work together.

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Solution

A complete the work in 45 days.
$∴ A's 1 day work = \frac{1}{45}$
A's 15 days work $= \frac{15}{45} = \frac{1}{3}$
Remaining work $= 1 - \frac{1}{3} = \frac{3 - 1}{3}$
B finishes $\frac{2}{3}$ rd work in 24 days
$\begin{matrix} B's 1 day work = \frac{\frac{2}{3}}{24} = \frac{2}{3 \times 24} = \frac{1}{36} (A + B)'s 1 day work = \frac{1}{45} + \frac{1}{36} \end{matrix}$

$= \frac{4 + 5}{180}$
$= \frac{9}{180}$
$= \frac{1}{20}$
Let $x$ days required
$∴ \frac{x}{20} = \frac{80}{100}$
$= x = \frac{80}{100} \times 20$
$= 16$ days

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A can do a work In 45 days. He works at it for 15 days and then, B alone finishes the remaining work in 24 days. Find the time taken to complete 80% of the work, if they work together.

A complete the work in 45 days. ∴ A's 1 day work =145 A's 15 days work =1545=13 Remaining work =1−13=3−13 B finishes 23 rd work in 24 days B's 1 day work =2324=23×24=136(A+B) 's 1 day work =145+136 =4+5180 =9180 =120 Let x days required ∴x20=80100 =x=80100×20 =16 days

A can do a work In 45 days. He works at it for 15 days and then, $B$ alone finishes the remaining work in 24 days. Find the time taken to complete $80 %$ of the work, if they work together.