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 the work in 12 days, find the time taken by B to finish the work.
Let the number of days in which B finishes the work be ‘b’.
∴ Number of days in which A finishes the work = b – 10
In 1 day,
B finishes 1/b of the work
A finishes 1/(b – 10) of the work
Now, both A and B together can finish the work in 12 days
⇒ 12(b – 10 + b) = b2 – 10b
⇒ 24b – 120 = b2 – 10b
⇒ b2 - 34b + 120 = 0
⇒ b2 -30b – 4b + 120 = 0
⇒ b(b – 30) – 4(b – 30) = 0
⇒ b = 4, 30 b can’t be 4 as A takes 10 days less than B
Thus number of days in which B alone finishes the work is 30 days.