Question

X , works equal to half of Y in 1/6 time . If 31 together they can complete a work in 10 days , then how many days will ' Y ' take to do the same work alone ?

Answer 1

Let Y does the whole work in a days

Work done by Y in 1 day = 1/a

According to the question: 

X does the half of 1/a work in a/6 days

X does the whole work in 2a/6 days = a/3 days

⇒ Work done by X in one day = 3/a

⇒ Work done by X and Y together in one day =1/a+3/a = 4/a

Time taken to complete the whole work by X and Y together = 1/4 = a/4 days

Again,

a/4 = 10

⇒ a = 40 days

∴ Time taken by Y in 40 days.

Y done in 40 days.