## A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days. In what time can A alone do it?

Question

A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and C can do it in 90 days. In what time can A alone do it?
I’ve calculated the total work don’t by all three and according to me it’s 60 days, I need help with the rest…​

in progress 0
1 week 2021-10-04T18:43:02+00:00 1 Answer 0 views 0

A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work?

[A]150 days

[B]80 days

[C]100 days

[D]120 dyas

120 days

(A+B)’s 1 day’s work = \frac{1}{72}

(B+C)’s 1 day’s work = \frac{1}{120}

(C+A)’s 1 day’s work = \frac{1}{90}

Adding all three, 2(A+B+C)’s 1 days work = \frac{1}{72}+\frac{1}{120}+\frac{1}{90}

=> \frac{5+3+4}{360}=\frac{12}{360}=\frac{1}{30}

∴ (A+B+C)’s 1 day’s work = \frac{1}{60}

Now, A’s 1 day’s work = (A+B+C)’s 1 day’s work – (B+C)’s 1 day’s work

=>\frac{1}{60}-\frac{1}{120}=\frac{2-1}{120}=\frac{1}{120}

∴ A alone can comlete the work in 120 days.

Hence option [D] is correct.