Test by Bikram | Mock GATE | Test 1 | Question: 64

Question

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 ________.

Comments

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

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should not it be 56?

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how please show your calculation ?

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sorry,i miscalculated..

Answer 1

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

Comments

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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Many thanks Harsh , i dont know how i missed that one!! pathetic mistake :( corrected and thanks for suggesting to frame better qstn :)