Question

Adya and Ashley complete a work separately in 20 and 25 days respectively. After 10 days of their working together, they both left then Amber came and completed the remaining work in 3 days. If Amber alone would do the work, calculate how many days he would take to complete the work.?​

Answer 1

$\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}$

Number of days Adya took to complete the work = 20

Work done by Adya in 1 day = $\frac{1}{20}$

Number of days Ashley took to complete the work = 25

Work done by Ashley in 1 day = $\frac{1}{25}$

So,

Total work by Adya & Ashley in 1 day =

$\frac{1}{20} + \frac{1}{20} \\ = \frac{5 + 4}{100} \\ = \frac{9}{100}$

•°• Their total work in 10 days =

$\frac{9 \times 10}{100} \\ = \frac{90}{100} \\ = \frac{9}{10}$

Now,

The work left to be completed =

$1 - \frac{9}{10} \\ = \frac{10}{10} - \frac{9}{10} \\ = \frac{1}{10}$

From this we know that,

Amber completes $\frac{1}{10}$ of the work in 3 days.

So,

Time taken by Amber to complete the whole work =

$3 \times 10 \\ = 30 \: \: days$

↦ If Amber alone would do the whole work, he would take $\boxed{30 \ \ days}$ to complete it.

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