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 ?

• A. 120 days
• B. 150 days
• C. 180 days
• D. 200 days

Answer 1

The correct option is A 120 days

(A + B)'s 1 days' work = $\frac{1}{72}$;

(B + C)'s 1 days work = $\frac{1}{120}$;

(A + C)'s 1 days' work = $\frac{1}{90}$

$\therefore (A+B{)}^{\prime }s+(B+C{)}^{\prime }s+(A+C{)}^{\prime }s$ 1 days work $=\frac{1}{72}+\frac{1}{120}+\frac{1}{90}=\frac{5+3+4}{360}=\frac{12}{360}=\frac{1}{30}$

$\Rightarrow 2(A+B+C{)}^{\prime }s$ 1 days' work $=\frac{1}{30}\Rightarrow (A+B+C{)}^{\prime }s$ $=\frac{1}{60}$

$\therefore$ A's 1 days' work = (A+B+C)'s 1 days' work - (B+C)'s 1 days' work

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

$\therefore$ A alone will complete the work in 120 days