Question

time taken by a person A alone to finish a work is 9 days less than the time taken by a person B alone to finish the same work. When they work together, they finish the same work in 20 days. In how many days A alone finish the work.

Answer 1

Answer:

Let A take x days to the work and so, B takes (x-9) days to do the same work. Together they can do it in 6 days, then how many days will A alone take to do the work?

A does 1/x th part of the work in a day, while B does 1/(x-9) th part of the work in a day. So A and B together do 1/x +1/(x-9) th or [x-9+x]/[x(x-9)] or [2x-9]/[x(x-9)] part of the work day in a day.

Hence [x(x-9)]/[2x-9] = 6.

x^2–9x = 12x-54, or

x^2–21x+54 = 0, or

(x-18)(x-3)=0, or x = 18. [3 is unacceptable as how can B do the same work in 3–9 or -6 days?]

So A does the work in 18 days and B does the same work in 9 days.

Check: 6[(1/18)+1/(18–9)] =6[(1/18)+(1/9)] = 6[3/18] = 1