Question

A and B together can do a job in $2$ days; B and C can do it in four days; and A and C in $2\frac{2}{5}$ days. The number of days required for A to do the job alone is:

• A. $1$
• B. $3$
• C. $6$
• D. $12$

Answer 1

Answer: (B)

$3$

Let A, B, C can do a job alone in a, b, c days.

A and B together can do in 2 days.

$\frac{1}{a}+\frac{1}{b}=\frac{1}{2}$ -------(1)

B and C together can do in 4 days.

$\frac{1}{b}+\frac{1}{c}=\frac{1}{4}$ ------(2)

C and A together can do in $\frac{12}{5}$ days.

$\frac{1}{c}+\frac{1}{a}=\frac{5}{12}$ -------(3)

(1) - (2), $⟹\frac{1}{a}-\frac{1}{c}=\frac{1}{4}$ -------(4)

(3) + (4), $⟹\frac{2}{a}=\frac{8}{12}$

$\therefore a=3$

$\therefore$ A can do job in 3 days.