(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?
A) 27 days B) 12 days C) 25 days D) 18 days
Answers
Given: (x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days.
To Find : in how many days can (x+10) men finish the work?
A) 27 days B) 12 days C) 25 days D) 18 days
Solution:
(x-2) men can do a piece of work in x days
=> Work = x(x - 2) man days
=> Work = x² - 2x man days
(x+7) men can do 75% of the same work in (x-10)days.
=> (75/100)Work = (x + 7)(x - 10) man days
=> (3/4) Work = x² - 3x -70 man days
=> Work = (4/3)x² - 3x -70 man days
x² - 2x = (4/3)x² - 3x -70
=> 3x² - 6x = 4x² - 12x - 280
=> x² - 6x - 280 = 0
=> x² - 20x + 14x - 280 = 0
=> (x - 20)(x + 14) = 0
=> x = 20 , x = - 14
Work = x² - 2x man days
= 20² - 2(20)
= 400 - 40
= 360 man day
(x+10) men = 20 + 10 = 30 Men
Number of Days = 360/30 = 12
(x+10) men finish the work in 12 Days
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