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
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Answer : 50
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 45 men for 52 weeks
c+52x = 45m*52 = 2340m ---(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 = 1560m
x = 40m ---(A)
Substituting this value in (2),
c + 13*40m = 780m
c = 260m ---(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)
260m +26*40m =nm * 26
1300m = 26nm
1300 = 26n
n = 1300/26 = 50
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 45 men for 52 weeks
c+52x = 45m*52 = 2340m ---(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 = 1560m
x = 40m ---(A)
Substituting this value in (2),
c + 13*40m = 780m
c = 260m ---(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)
260m +26*40m =nm * 26
1300m = 26nm
1300 = 26n
n = 1300/26 = 50
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