Discussion

Question:

A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in two-third the time. How many workers were there in the group?

Explanation:

Let the work done by a worker be x units, w be the total work and n be the number of workers in the group.

Then, w = Work done on the nth day i.e. last day + Work done on the second last day + … + Work done on the first day

⇒ w = x + 2x + ... + nx = $\frac{n (n + 1) x}{2}$ ...(i)

When none of the workers is removed, then

w = nx × $\frac{2 n}{3} = \frac{2 n^{2} x}{3}$ ...(ii)

From equation (i) and (ii), we get

$\frac{n (n + 1) x}{2} = \frac{2 n^{2} x}{3}$

⇒ n = 3.

Hence, option (b).

» Your doubt will be displayed only after approval.

Discussion

Doubts

Feedback