A piece of work can be done by 10 boys . . ..

Vincen wrote:A piece of work can be done by 10 boys in 6 days working 4 hours each day. How many minimum possible number of boys are needed to complete another work which is three times more if they work for same integer number of hour and day, say x hour and x days?
(1) 5
(2) 10
(3) 12
(4) 15
(5) 30

The OA is option D.

I got confused here. I'd like the explanation of an expert. Thanks in advanced.

If 10 boys can do a work in 6 days while working 4 hours a day
then one boy will do the same work in 10x6x4= 240 hours.

the new work is three times more
=> one boy will do three times more work in 240 + 240x3 =960 hours

further let Y be the minimum number of boys working x hours a day for x days to complete the new work
then Y = 960/x^2 or Y*x^2 = 960

now we have to find the maximum value of x which should be an integer so as to get the Y as an integer

that value we can find by making factors of 960 in the form Y*x^2
960 x 1^2
240 x 2^2
120 x 4^2
15 x 8^2
Thus the maximum value of x is 8 and the minimum value of Y is 15

Hence option (4) is correct.