A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of a man, a woman and a child are in the ratio 5 : 4 : 2, then a 16 hectare field will be reaped by 6 men, 4 women and 7 children in = ?
Correct Answer: 8 days
According to the question,
Efficiency of a man, a woman and a child are
$$\eqalign{ & 5:4:2{\text{ units/day}} \cr & {\text{One day work of 2 men}} \cr & = 2 \times 5 \cr & = 10{\text{ units}} \cr & {\text{One day work of 3 women}} \cr & = 3 \times 4 \cr & = 12{\text{ units}} \cr & {\text{One day work of 4 children}} \cr & = 4 \times 2 \cr & = 8{\text{ units}} \cr} $$
Applying formula, let time taken is D days.
$$\frac{{\left( {10 + 12 + 8} \right) \times {{10}_{{\text{days}}}}}}{{{{10}_{{\text{hectare}}}}}} = $$ $$\left$$
$$\eqalign{ & \Leftrightarrow \frac{{\left( {30} \right) \times 10}}{{10}} = \frac{{\left \times {\text{D}}}}{{16}} \cr & \Leftrightarrow {\text{D}} = 8{\text{ days}} \cr} $$
Efficiency of a man, a woman and a child are
$$\eqalign{ & 5:4:2{\text{ units/day}} \cr & {\text{One day work of 2 men}} \cr & = 2 \times 5 \cr & = 10{\text{ units}} \cr & {\text{One day work of 3 women}} \cr & = 3 \times 4 \cr & = 12{\text{ units}} \cr & {\text{One day work of 4 children}} \cr & = 4 \times 2 \cr & = 8{\text{ units}} \cr} $$
Applying formula, let time taken is D days.
$$\frac{{\left( {10 + 12 + 8} \right) \times {{10}_{{\text{days}}}}}}{{{{10}_{{\text{hectare}}}}}} = $$ $$\left$$
$$\eqalign{ & \Leftrightarrow \frac{{\left( {30} \right) \times 10}}{{10}} = \frac{{\left \times {\text{D}}}}{{16}} \cr & \Leftrightarrow {\text{D}} = 8{\text{ days}} \cr} $$