Question

Q.1) B takes 16 days less than A to do a piece of work. If both working together can do it in 15 days, in how many days will B alone complete the work? 
A.  20 days, b. 22 days,  c. 24 days, d. 26 days​

Answer 1

Answer:

Let A take x days to the work. It means A does (1/x)th part of the work in 1 day.

Then B takes (x-16) days to do the same work, or B does 1/(x-16)th part of the work in 1 day.

Thus A and B do (1/x) + 1/(x-16) = (x-16+x)/x(x-16) or (2x-16)/x(x-16) th part of the work in 1 day.

Or A and B take x(x-16)/(2x-16) days = 15 days.

x(x-16) = 15(2x-16)

x^2–16x = 30x-240, or

x^2–46x+240 = 0

(x-40)(x-6)=00

x = 40 or 6. Here 6 is too less a figure and so not acceptable.

So A takes 40 days and B takes 24 days to do the same work. Answer.

Check: 1/40 + 1/24 = (24+40)/(40*24) = 64/960 = 1/15 of the work in one day

hope it helps

thank you