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A contractor receives a certain sum that he uses for paying wages. His capital, together with the weekly subsidy, 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 subsidy would just suffice for $13$ weeks. How many men can he maintain for $26$ weeks?

  1. $48$
  2. $80$
  3. $68$
  4. $30$
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Let C be the capital in fixed amount
W be the weekly subsidy and ‘s’ be the weekly wage for each man.
Then from given condition (first), C + 52W = 42 × 52s...........(1)

From second condition C + 13W = 13 × 60s...........(2)
Solving (1) and (2) we get
39 W = 1404 s
W = 36s
and 3C = 3120 - 2184 = 936 s or C = 312 s

For 13 weeks, C +26w = m* 26s
312 s+ 936 s = m *26s

1248 s = m * 26 s

m = 1248/26 = 48
=> m= 48
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