A group of men decided to do a job in 13 days but 9 men left the work after each day. The work, as a result, got completed in 16 days. How many men were initially in the group?

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Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 1)

Answer 1

Given:

A group of men decided to do a job in 13 days.

Formula used:

Total work = efficiency × time

Sum of n terms = n/2 × [a + l]

Where, n = number of terms;

a = first term; l = last term

Calculation:

Let the number of person in group initially = x

9 men left work after each day.

So it becomes an A.P series.

⇒ x + (x -9) + (x - 18)............ (x - 135) = x × 13

⇒ (16/2) × [x + x - 135] = 13x

⇒ 8 × [2x - 135] = 13x

⇒ 16x - (135 × 8) = 13x

⇒ 16x - 13x = 135 × 8

⇒ x = (135 × 8)/3 = 45 × 8 = 360 persons.

∴ The correct answer is 360 persons.

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