Question

A can do a piece of work in 25 days. when he had worked for 10days B join him.if he complete work was finished in 20 days. in how many days B alone can finish the work​

Answer 1

Given :- A can do a piece of work in 25 days. when he had worked for 10 days B join him. if he complete work was finished in 20 days.

To Find :- In how many days B alone can finish the work ?

Solution :-

→ In 25 days A can do = 1 work

→ In 1 day A can do = (1/25) work

→ In 10 days A can do = (1/25) × 10 = (10/25) = (2/5) work .

So,

→ Left work to be done = 1 - (2/5) = (3/5) work .

Now, let us assume that, A can finish the work alone in x days .

So,

→ Per day work of B = (1/x)

then,

→ Per day work of (A + B) = (1/25) + (1/x) = {(x + 25)/25x}

given that, in next 10 days both A and B finishes the remaining work . { 20 - 10 = 10 days. }

therefore,

→ 10{(x + 25)/25x} = 3/5

→ (2/5x)(x + 25) = 3/5

→ 2(x + 25) = 3x

→ 2x + 50 = 3x

→ 3x - 2x = 50

→ x = 50 days (Ans.)

Verification :-

→ 10(1/25) + 10(1/25 + 1/50) = 1

→ (2/5) + 10(3/50) = 1

→ (2/5) + (3/5) = 1

→ (5/5) = 1

→ 1 = 1

→ LHS = RHS

Hence, B alone can finish the total work in 50 days .

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