Aptitude Question ID: 106002
A and B working together can do a piece of work in $latex 4\frac{1}{2}\ hours&s=1$. B and C working together can do it in 3 hours. C and A working together can do it in $latex 2\frac{1}{4}\ hours&s=1$. All of them begin the work at the same time. Find how much time they will take to complete the piece of work :
[A]2 hours
[B]2.5 hours
[C]3 hours
[D]3.25 hours
2 hours
(A + B)’s 1 hour’s work $latex = \frac{2}{9}&s=1$……….(I)
(B + C)’s 1 hour’s work $latex = \frac{1}{3}&s=1$…….….(II)
(C + A)’s 1 hour’s work $latex = \frac{4}{9}&s=1$……….(III)
On adding,
2(A + B + C)’s 1 hour’s work $latex = \frac{2}{9}+\frac{1}{3}+\frac{4}{9} = \frac{2+3+4}{9} = 1&s=1$
∴ A, B and C together will complete the work in 2 hours.
Hence option [A] is correct answer.