Question

$6$ pumps can irrigate a large farm in $4$ days if work for $8$ hours each day. How many minutes each day did $5$ pumps work if the same farm was irrigated in $12$ days?

Answer 1

Part of farm irrigated if $6$ pumps work for $4$ days and $8$ hours each day $=1$

That is, Part of farm irrigated if $6$ pumps work for total $4\times 8=32$ hours is $=1$

Part of farm irrigated if $6$ pumps work for $1$ hour is $=\frac{1}{32}$

Part of farm irrigated if $1$ pump work for $1$ hour is $=\frac{1}{32\times 6}$

Let $5$ pumps work for $x$ hours each day, to irrigate the farm in $12$ days.

Now,

Part of farm irrigated if $5$ pump work for $1$ hour is $=\frac{5}{32\times 6}$

Part of farm irrigated if $5$ pump work for $12x$ hour is $=\frac{5\times 12x}{32\times 6}$$=\frac{5x}{16}$

So,

$\frac{5x}{16}=1$

$x=\frac{16}{5}$ hours

$x=\frac{16}{5}\times 60$ minutes $=192$ minutes