A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 233 days, `4/7` of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day? `80` b. `82` c. `81` d. `83`

Options

A. 80
B. 81
C. 82
D. 83

Answer

(b)

Explanation

Let `x` additional men employed.
117 men were supposed to finish the whole work in
`46xx8= 368` hours.
But 117 men complete `4/7` of the work in `33 xx 8 `
= 264 hours
`therefore` 117 men could complete the work in 462 hours.
Now `(117 + x)` men are supposed to do `3/7` of the work,
working 9 hours a day, in `13xx 9 = 117` hours, so as to
finish the work in time.
i.e. `(117 + x )` men are supposed to complete the whole
work in `117 xx 7/3 = 273` hours.
`therefore (117+ x) xx 273 = 117 xx 462`
`rArr (117 + x)xx 7 = 3 xx 462`
`rArr x+ 117 = 3 xx 66 = 198 rArr x = 81`
`therefore` Required number of additional men to finish the
work in time = 81.