Multiple choice

𝑁 men of equal efficiencies can do a certain work in 20 days. Instead, if starting from day 2, each day 5 men of same efficiencies as that of each person in the initial group joins the group, then the work would be over in 15 days. The value of 𝑁 is equal to

  1. 10

  2. 105

  3. 80

  4. 120
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = 20N. With the new plan, the number of men is N, N+5, N+10, ..., N+14*5. This is an arithmetic progression for 15 days. Total work = sum of men over 15 days = (15/2) * [2N + (15-1)*5] = (15/2) * [2N + 70] = 15(N + 35) = 15N + 525. Equating: 20N = 15N + 525 => 5N = 525 => N = 105.

AI explanation

Let the total work be 20N units, where N is the initial number of men. In the second scenario, the men work for 15 days, with 5 additional men joining each day starting from day 2. The number of men working on day 1 is N, on day 2 is N plus 5, on day 3 is N plus 10, and so on, until day 15 where the number of men is N plus 70. The total work done is the sum of this arithmetic progression, which is 15 divided by 2 multiplied by the sum of the first and last terms. This gives a total of 15 divided by 2 multiplied by (2N plus 70), equaling 15N plus 525. Setting this equal to the total work of 20N gives 15N plus 525 equals 20N. Solving for N gives 5N equals 525, so N equals 105. The correct answer is 105.

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