Question

Aand B together can do a piece of work in 15 days , while B alone can finish it 20days.In how many days can A alone finish the work
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Answer 1

Given:

• A and B together can do a piece of work in 15 days.

• B alone can finish it 20days.

To find:

• In how many days A can alone finish the work.

Solution:

Let us assume that A's alone work be a.

From the question,

$\sf \bf \tt{ \frac{20a}{20 + a} = 15}$

$\sf\longrightarrow \: \: {20a = 15(a + 20)}$

$\sf\longrightarrow \: \: {20a = 15a + 300}$

$\sf\longrightarrow \: \: {20a - 15a = 300}$

$\sf\longrightarrow \: \: {5a = 300}$

$\sf\longrightarrow \: \: {a = \frac{ \cancel{{300}}}{\cancel{5}}}$

$\orange{\longrightarrow\: \: \pmb{a = 60}}$

Therefore,

• In 60days A can alone finish the work.