Question

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

Answer 1

Hint:
We have been given that $$\;6$$ pumps can irrigate a large farm in $$4$$ days if work for $$8$$ hours each day. we have to consider $$x$$ for an hour in a day in which far will irrigate in 12 days. Then the equation will be formed. After solving the equation we will get the correct answer.

Complete step by step solution:
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 $$ = 321$$​
Part of farm irrigated if $$1$$ pump work for $$1$$ hour is $$ = 32 \times 61$$​
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 $$ = 32 \times 65$$
Part of farm irrigated if 5 pump work for $$12x$$ hour is $$ = 32 \times 65 \times 12x = 165x$$
So,
$$165x = 1$$
$$x = 516$$​ hours

$$x = 516 \times 60$$ minutes
$$ = 192\;$$ minutes

Note:
From the given data, we make an equation by considering $$x$$ for an hour in a day in which far will irrigate in 12 days. After solving the equation we got the correct answer i.e. it will require 192 minutes each day to do pump work if the same farm was irrigated in $$12$$ days.