Question

A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days can the two of them complete the work together ?

• A. 20 days
• B. 25 days
• C. 30 days
• D. 35 days

Answer 1

The correct option is C 30 days

A's 1 days' work $=\frac{1}{80}$

A's 10 days' work $=\frac{10}{80}=\frac{1}{8}$

Remaining work $=1-\frac{1}{8}=\frac{7}{8}$

$\frac{7}{8}$ of the work is completed by B in $42$ days

$\therefore$ The whole work is completed by B in $\frac{42\times 8}{7}$ days = $48$ days

$\therefore$ B's 1 days' work $=\frac{1}{48}$

(A + B)'s 1 days' work $=\frac{1}{80}+\frac{1}{48}=\frac{3+5}{240}=\frac{8}{240}=\frac{1}{30}$

$\therefore$ A and B can complete the whole work together in $30$ days