Question

$A$ can cultivate $\frac{2}{5}$ of a land in 6 days and $B$ can cultivate $\frac{1}{3}$ of the same land in 10 days. Working together, $A$ and $B$ can cultivate $\frac{4}{5}$ of the land in:

• A. 4 days
• B. 5 days
• C. 8 days
• D. 10 days

Answer 1

The correct option is C 8 days

$A$ can cultivate the full part of the land in $\frac{6\times 5}{2}$ days $=15$ days
$B$ can cultivate the full part of the land in $(10\times 3)=30$ days
$\therefore$ Part of the land cultivated by $(A+B)$ in 1 day $=\left(\frac{1}{15}+\frac{1}{30}=\frac{2+1}{30}=\frac{3}{30}\right)=\frac{1}{10}$
$\frac{1}{10}$ part of the land is cultivated by $(A+B)$ in 1 day
$\therefore \frac{4}{5}$ part of the land will be cultivated by $(A+B)$ in $10\times \frac{4}{5}$ days $=8$ days.