Question

A and B working together can do 30% of the work in 6 days. B alone can do the same work in 25 days. How long will A alone take to complete the same work?
1. 75 days
2. 60 days
3. 100 days
4. 80 days

Answer 1

Correct Answer - Option 3 : 100 days

Given:

30% of the work is done by A and B together in 6 days.

B can do the same work in 25 days.

Concept used:

If a person does work in n days,

then one day work by a person = 1/n part of the total work.

Calculation:

Let A can do a task in x days.

then A one day work = 1/x part of a work.

And B one day work = 1/25 part of a work.

A and B 30% of a work = 6 days

⇒ A and B do a work = (6/30) × 100

⇒ A and B do a work = 100/5 days

⇒ A and B do a work = 20 days

∴ one daywork of A and B = 1/20 parts of a work

According to question:

1/x + 1/25 = 1/20

⇒ 1/x = (1/20) – (1/25)

⇒ 1/x = (5 – 4)/100

⇒ 1/x = 1/100

∴ x = 100 days

Hence, A alone can do the same work in 100 days.