Question

A $10$ hectare field is reaped by $2$ men, $3$ women and $4$ children in $10$ days. If a man, a woman and a child work in the ratio $5:4:2,$ a $16$ hectare field will be reaped by $6$ men, $4$ women and $7$ children in:

• A. $5$ days
• B. $6\frac{1}{2}$ days
• C. $7$ days
• D. $8$ days

Answer 1

Answer: (D)

$8$ days

Man:Woman:child = $5:4:2$
Man:Woman = $5:4$
$4$ men = $5$ women
Man:Child = $5:2$
$2$ men = $5$ children
Woman:Child = $4:2$
$4$ children = $2$ women
Or $1$ woman = $2$ child
$2$men, $3$ women and $4$ children = $5+6+4$ children = $15$ children
$15$ children reap $10$ hectare field in $10$ days
Now $6$ men, $4$ women and $7$ children: $3\times 5+4\times 2+7$ children = $15+15$ = $30$ children
We need to find time taken by $30$ children to reap $16$ hectares
We know that $15$ children reap $10$ hectare field in $10$ days
$15$ children will reap 1 hectare in $\frac{10}{10}=1$ day
$15$ children will reap $16$ hectare in $1\times 16=16$ days
$30$ children will reap $16$ hectare in $\frac{16}{2}=8$ days
i.e $6$ men, $4$ women and $7$ children will reap $16$ hectares in $8$ days