A takes 10 days less than the time taken by B to finish a piece of wor

1.	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.
Answer» 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 \(\Rightarrow \frac{1}{b}+\frac{1}{b\,-10}=\frac{1}{12}\) ⇒ 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.

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.

Answer»

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

\(\Rightarrow \frac{1}{b}+\frac{1}{b\,-10}=\frac{1}{12}\)

⇒ 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.