A alone can do a piece of work in 30 days. He worked at it for 5 days and then B alone finished the remaining work in 10 days. In how many days B alone can finish the entire work?

Question

Question

This question was previously asked in

SSC MTS (2022) Official Paper (Held On: 10 May, 2023 Shift 1)

Answer 1

Given:

A's work rate = 1/30 (A can do the work in 30 days)

A worked for 5 days

B finished the remaining work in 10 days

Formula:

Work rate × Time = Work done (1 job)

Calculation:

Work done by A = (A's work rate) × (Time A worked) = (1/30) × 5 = 5/30 = 1/6

Now, the remaining work to be done when B takes over is 1 - 1/6 = 5/6.

Let "x" be the number of days B takes to complete the remaining work:

(B's work rate) × x = 5/6

(B's work rate) × 10 = 5/6 (B finishes the remaining work in 10 days)

Now, let's find B's work rate:

(B's work rate) × 10 = 5/6

(B's work rate) = (5/6) / 10 = 5/60 = 1/12

Now that we know B's work rate, we can find how many days B alone can finish the entire work:

(B's work rate) × Time = 1

(1/12) × Time = 1

Time = 12 days

So, B alone can finish the entire work in 12 days.