To do a certain work, the ratio of efficiencies of X and Y is 5 : 7. Working together, X and Y can complete the same work in 70 days. X alone started the work and left after 42 days. Y alone will complete the remaining work in:

90 days

Given,

                  X  :  Y 

Efficiency     5  :  7

⇒ X + Y in 70 days complete the whole work = (5 + 7) x 70 = 840 units  ..(Efficiency × Days = Total work)

⇒ X left after 42 days = 5 x 42 = 210 units,

⇒ Remaining work = 840 - 210 = 630 units,

⇒ Time taken by Y to complete the remaining work = \(\frac{630}{7}\) = 90 days.       ..(\(\frac{Work}{Efficiency}\) = Time)