Time & Work

X can finish a work in 3 days less than that of Y, X alone worked for 4 days and the remaining work was completed by Y. If the whole work took 14 days, in how many days can X and Y alone complete the work ?

** Option:**

**A.**12, 14

**B.**14, 16

**C.**16, 12

**D.**12, 15

**Answer: D . 12, 15**

** Justification:**

Suppose Y can finish a work in x days.

X can finish the work in (x - 3) days.

X's 1 day's work = $1/{x - 3}$

X's 4 days work = $4/{x - 3}$

Remaining work = $1 - {4/{x - 3}}$ = ${x - 7}/{x - 3}$

Y can finish 1 work in x days.

Y can finish 1 work in ${x - 7}/{x - 3}$ = $ x *{x - 7}/{x - 3}$ days.

By hypothesis,

$x *{x - 7}/{x - 3} + 4$ = 14

$x^2 - 17x + 30 = 0$

x = 2 or X = 15

So,X can finish the work in 15 days.

Y can finish the work in x - 3 = 15 - 3 = 12.

Hence, X and Y can individually finish the work in 15 or 12 days respectively.