I don't know how to solve this.Kindly solve this.

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A contractor receives a certain sum that he uses to pay wages. His capital, together with the weekly subsidy, would eactly enable him to pay $42$ men for $52$ weeks. If he had $60$ men at the same weekly* *wages, his capital together with the weekly subsidy would exactly suffice for $13$ weeks. The number of men who can be maintained for $26$ weeks is ________.

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Best answer

Let the contractor's capital be c and his weekly sum of be x

Let payment needed for one man one week = m

His own capital together with the weekly sum enables him to pay 42 men for 52 weeks

c + 52x = 42m * 52 = 2184 m ---(1)

If he had 60 men and the same wages, his capital and weekly sum would suffice for 13 weeks

c+13x = 60m*13 = 780m ---(2)

(1)-(2) => 39x = 1404 m

x = 36 m ---(A)

Substituting this value in (2),

c + 13 * 36 m = 780m

c = 312 m ---(B)

Let n men can be maintained for 26 weeks.

c + 26x = nm * 26

Substituting the values of c and x in the above equation from (A) and (B)

312 m +26 * 36m =nm * 26

1248 m = 26nm

1248 = 26n

then

n = 1248 /26

= 48

Let payment needed for one man one week = m

His own capital together with the weekly sum enables him to pay 42 men for 52 weeks

c + 52x = 42m * 52 = 2184 m ---(1)

If he had 60 men and the same wages, his capital and weekly sum would suffice for 13 weeks

c+13x = 60m*13 = 780m ---(2)

(1)-(2) => 39x = 1404 m

x = 36 m ---(A)

Substituting this value in (2),

c + 13 * 36 m = 780m

c = 312 m ---(B)

Let n men can be maintained for 26 weeks.

c + 26x = nm * 26

Substituting the values of c and x in the above equation from (A) and (B)

312 m +26 * 36m =nm * 26

1248 m = 26nm

1248 = 26n

then

n = 1248 /26

= 48

Sir,

answer should be 48 ,

**In eqaution (1) you took number of men = 45 , whereas in the question its 42.**

Sir and one small edit in the question might make the question more clearer ,

*"If he had 60 men at the same weekly wages, his capital together with the weekly subsidy would just suffice for 13 weeks."*

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