Four boys and ten girls can cut a field in 5 hours if the boys work at $\frac{5}{4}$ the rate at which the girls work. How many boys will be needed to cut the field in 3 hours?

180

Correct answer is D

Let x represents number of boys that can work at $\frac{5}{4}$ the rate at which the 10 girls work

For 1hr. x boys will work for $\frac{\frac{1}{5}}{4}$ x 10

x = $\frac{4}{5}$ x 10 = 8 boys

8 boys will do the work of ten girls at the same rate 4 + 8 = 12 boys cut the field in 5 hrs

For 3 hrs, $\frac{12 \times 5}{3}$ boys will be needed = 20 boys

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