A and B can do a piece of work in 10 days and 15 days respectively. A alone starts the work. Then, 5

A and B can do a piece of work in 10 days and 15 days respectively. A alone starts the work. Then, 5 days after he is joined by B. In how many days, work will be completed ?

A. 7

B. 8

C. 11

D. 12

E. None of the above

Answer: B. 8

A's 1 day's work = $1/10$
B's 1 day's work = $1/15$
A's 5 day's work = $5/10 = 1/2$
Remaining work to be done by both A and B = $ 1 - 1/2 = 1/2$
Now, (A + B)'s 1 day's work = $ 1/10 + 1/15$
= ${3 + 2}/30 = 5/30 = 1/6$
$1/6$ work is done by A and B in = 1 day.
$1/2$ work is done by A and B in = ${1 × 6 × 1}/ {1 × 2}$ = 3
Hence, total number of days taken to finish the work = 5 + 3 = 8 days.

Posted in: Time & Work - Aptitude - Mathematics