Question

If a farmer harvests his crops in 7 days and his wife harvests the same amount of crops in 5 days then in how many days will the same amount of crops be harvested if both husband and wife work together?

• A. $\frac{5}{12}$ days
• B. $\frac{35}{12}$ days
• C. $\frac{7}{12}$ days
• D. $\frac{12}{35}$ days

Answer 1

The correct option is B $\frac{35}{12}$ days

The farmer harvests his crops in 7 days.
So in one day, he harvests ${\frac{w}{7}}^{th}$ of the crop where w is the total crops to be harvested.
His wife harvests the same amount in 5 days.
So in one day she harvests ${\frac{w}{5}}^{th}$ of the crop
So adding both of their works of one day, we get = ${\frac{w}{7}}^{th}$+${\frac{w}{5}}^{th}$ =${\frac{5w+7w}{7\times 5}}^{th}$
i.e. ${\frac{12w}{35}}^{th}$ of the crop
So total work done = $\frac{1}{oneda{y}^{\prime }swork}$
So Total harvest will be completed in $\frac{35}{12}$ days