Question

A can do a piece of work in x days and B can do it in ( x + 16 ) days. If both working together can do it in 15 days, thenthe value of x is
(a) 16
(b) 24
(c) 26
(d) 28​

Answer 1

Answer:

(b) 24

Work done by A in one day = 1/x

Work done by B in one day = 1/(x + 16)

Therefore, work done by both together in a day is given by

=> 1/x + 1/(x+16) = 1/15

=> (2x + 16)/(x² + 16x) = 1/15

=> 30x + 240 = x² + 16x

=> x² - 14x - 240 = 0

=> x² - 24x + 10x - 240 = 0

=> x (x - 24) + 10 (x - 24) = 0

=> x = 24 or - 10

Since number of days can't be negative.

=> x = 24