Question

A can do a piece of work in 'x' days and B can do the same work in (x+16) days. If been working together can do it in 15 days; calculate 'x'.​

Answer 1

Answer:

x = 24.

Step-by-step explanation:

No. of days taken by A to complete the work alone = x days

No. of days taken by B to complete the work alone = (x+16) days

Part of work done by A and B together in 1 day = 1/x + 1/(x+16)

                                                                               = (2x + 16/x² + 16x) part

It is given that,

15 = x² + 16x/2x + 16

30x + 240 = x² + 16x

x² - 14x - 240 = 0

x² + 10x - 24x - 240 = 0

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

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

Hence, x = (-10) or x = 24.

But, no. of days can never be negative, so we will reject x=(-10).

Hence, A takes 24 days to complete the work alone and B takes 40 days to do so alone.

Hope it helps you....