X alone can do a work in 300 hours. Y alone can do the same work in 450 hours. X, Y and Z together can do the same work in 90 hours. In how many hours can Z alone do the work?

X alone can do a work in 300 hours. Y alone can do the same work in 450 hours. X, Y and Z together can do the same work in 90 hours. In how many hours can Z alone do the work? Correct Answer 180

GIVEN:

X alone can do a work = 300 hours

Y alone can do the work = 450 hours

X, Y and Z together can do the work = 90 hours

FORMULA USED:

Z alone can do a work = (X + Y + Z) one hour work - X’s one-hour work - Y one- hour work

CALCULATION:

X’s one-hour work = 1/300

Y alone can do the work = 450 hours

Y one- hour work = 1/450

X, Y and Z together can do the work = 90 hours

(X + Y + Z)’s one-hour work = 1/90

Z alone can do the work in,

Z = (1/90 - 1/300 - 1/450) = (10 - 3 - 2)/900 = 5/900 = 1/180