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Question
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.
Solution
Let B takes x days to complete the work.
Therefore, A will take `(x-10)`days.
∴`1/x+1/((x-10))=1/12`
⇒`((x-10)+x)/(x(x-10))=1/12`
⇒`(2x-10)/(x^2-10x)=1/12`
⇒`x^2-10x=12(2x-10)`
⇒`x^2-10x=24x-120`
⇒`x^2-34x+120=0`
⇒`x^2-(30+4)x+120=0`
⇒`x^2-30x-4x+120=0`
⇒`x(x-30)-4(x-30)=0`
⇒`(x-30)(x-4)=0`
⇒`x=30 or x=4`
Number of days to complete the work by
B cannot be less than that by A; therefore, we get: x = 30
Thus, B completes the work in 30 days.
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