Problem Solving

vaibhav101 wrote:16 men can complete a work in 12 days. 24 children can complete the same work in 18 days. 12 men and 8 children started working and after 8 days 3 more children joined them. How many days will they now take to complete the remaining work?

A 2
B 4
C 6
D 8
E 10

Since 16 men working for 12 days are the equivalent of 24 children working for 18 days, we get:
(16m)(12) = (24c)(18)
4m = 9c
m = (9/4)c.

Let the rate for each child = 4 units per day, implying that the rate for each man = (9/4)(4) = 9 units per day.
Since 24 children complete the job in 18 days, we get:
Total work = (number of children)(rate per child)(number of days) = (24)(4)(18) = 1728 units.

Rate for 12 men and 8 children = [(number of men)(rate per man)] + [(number of children)(rate per child)] = (12*9) + (8*4) = 140 units per day.
In 8 days, the amount of work produced = rt = 140*8 = 1120 units.
Remaining work = 1728 - 1120 = 608 units.

When 3 children are added -- each producing 4 units per day -- the daily rate in green increases by 12 units to 152 units per day.
Time to produce the remaining 608 units = w/r = 608/152 = 4 days.

The correct answer is B.