Question

4. A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together
can finish it in 12 days, find the time taken by B to finish the work​

Answer 1

Answer:

let's assume that B can finish the work in x days

A takes 10 days less than that of B.

so A takes x-10 days to complete the work.

1/A+1/B=1/12

1/(x-10)+1/x=1/12;

(x-10+x)/(x²-10x)=1/12

24x-120=x²-10x

x²-34x+120=0

x²-4x-30x+120=0

x(x-4)-30(x-4)=0

x=4 or x=30

x cannot be 4

because it is the time taken by B. we have to subtract 10 from it to get the time taken by A.

so x=30

work can be done by B in 30 days.

A is 20 days.