Question

A and B can do a job together in 25 days. After 15 days of working together, B leaves. If A completes the remaining part of the job in 20 days, how long would each take to complete the job, working separately?​

Answer 1

Answer:

1. A takes 50 days to complete the work.
2. B also takes 50 days to complete the work.

Step-by-step explanation:

Given that:

• A and B can do a job together in 25 days.
• After 15 days of working together, B leaves.
• A completes the remaining part of the job in 20 days.

To Find:

• How long would each take to complete the job working separately?

We know that:

• Total work = 1

• A and B's 25 days work = 1
• A and B's one day work = 1/25

A and B working together for 15 days,

• A and B's 15 days work = 15/25 = 3/5

Remaining work = Total work - work done

• Remaining work = 1 - 3/5
• Remaining work = 5/5 - 3/5
• Remaining work = 2/5

Remaining work completed by A in 20 days,

• A's 20 days work = 2/5
• A's one day work = 2/(5 × 20) = 1/50
• A's 50 days work = 50/50 = 1

So, A can complete a work separately in 50 days.

Let B can complete the work separately in x days.

• B's one day work = 1/x

A's one day work + B's one day work = (A + B)'s one day work

→ 1/50 + 1/x = 1/25

→ 1/x = 1/25 - 1/50

→ 1/x = 2/50 - 1/50

→ 1/x = 1/50

→ x = 50

Therefore,

• B can complete the work separately in 50 days.

Answer 2

Given :- A and B can do a job together in 25 days. After 15 days of working together, B leaves. If A completes the remaining part of the job in 20 days .

To Find :- How long would each take to complete the job, working separately ?

Solution :-

Let's solve this problem in a very simple way.

given that,

→ In 25 days (A + B) completes = 1 work.

so,

→ In 1 day (A + B) completes = (1/25) work .

then,

→ In 15 days they completes = (1/25) * 15 = (3/5) work .

so,

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

given that,

→ Left (2/5) work done by A alone in = 20 days.

then,

→ Total 1 work will done by A alone in = 20 * (5/2) = 50 days (Ans.)

therefore,

→ Total 1 work done by B alone in = (1/25) {A + B / day work} - (1/50){ A alone / day work.} = (1/25) - (1/50) = 50 days. (Ans.)

Hence, Both A and B will take 50 days to completes the Job when working separately .

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