Multiple choice

A contractor receives weekly payments for work done that he uses for paying wages. His capital, together with the weekly payment, would just enable him to pay 42 men for 52 weeks. If he had 60 men at the same wage, his capital, together with the weekly payment, would just suffice for 13 weeks. How many men can be maintained for 26 weeks?

  1. 60

  2. 55

  3. 50

  4. 48

  5. 35
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let C be capital and W be weekly payment. C + 52W = 42 * 52 * w (where w is wage per man). C + 13W = 60 * 13 * w. Solving for C and W in terms of w: C + 52W = 2184w and C + 13W = 780w. Subtracting: 39W = 1404w, so W = 36w. Then C = 780w - 13(36w) = 780w - 468w = 312w. For 26 weeks: C + 26W = N * 26 * w. 312w + 26(36w) = 26Nw. 312 + 936 = 26N. 1248 = 26N. N = 48.

AI explanation

Let the capital be C and the weekly payment be P. The equation for 42 men for 52 weeks is C + P = 2184 wages, and for 60 men for 13 weeks it is C + P = 780 wages. Equating both gives 2184w = 780w + P, resulting in the weekly payment P being equivalent to 1404 wages. Substituting this back yields the capital C as 3900 wages, making the total funds 3900 + 1404 = 5304 wages. For 26 weeks, the total wage requirement is 26M, so equating 26M = 5304 gives M = 48.

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