A and B working alone can do a work in 40 days and 30 days, respectively. They started the work together, but B left after some time and A finished the remaining work in 5 days. How many days after starting did B leave the work?

Question

Question

This question was previously asked in

RRB Technician Grade III Official Paper (Held On: 28 Dec, 2024 Shift 2)

Answer 1

Given:

A and B can do a work in 40 and 30 days respectively.

A and B began the work together.

After some days B left, A finished the remaining in 5 days

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day

Calculation:

Let, after x days B leave.

Let the total work is the 120 units (LCM of 30 and 40)

Efficiency of A is 120 / 40 = 3 units

Efficiency of B is 120 / 30 = 4 units

So, for x days they both work together.

According to the question,

(3 + 4) × x + 5 × 3 = 120

⇒ 7x + 15 = 120

⇒ x = 15 days

∴ B leaves after 15 days.

Additional Information

Efficiency of a person is inversely proportional to number of days to complete the work.