Linear Equation 29

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A and B together can do a piece of work in 15 days. If one day's work of A be 3 / 2 times one day's work of B,
find in how many days, each alone will do the work.

Solution:

Let A alone will do the work in x days and B alone will do the same work in y days.

Therefore, 1 / x + 1 / y = 1 / 15 ---------------------- (i)

and 1 / x = 3 / 2 X 1 / y

=> 1 / x - 3 / 2 y = 0 --------------------------------- (ii)

On solving equations (i) and (ii), we get

x = 25 and y = 37.5

Therefore, A alone will do the work in 25 days and

B alone will do the work in 37.5 days