EduGoog

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.

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