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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?


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

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 $$=\cfrac{5}{32\times 6}$$

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

So, 
$$\cfrac{5x}{16}=1$$
$$x=\cfrac{16}{5}$$ hours

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

Mathematics

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