Question

The amount of time it takes to consume green grass of a filed is inversely proportional to the number of goats present. If there are $4$ goats, then it takes $20$ days to consume the grass. How much less time will it take if there are $5$ goats?

• A. $4$ days
• B. $\frac{3}{4}$ week
• C. $18$ hours
• D. $4$ hours

Answer 1

The correct option is A $4$ days

Let 'T' denote the time taken and 'N' denote the number of goats.

Then

$T\propto \frac{1}{N}$ or $T_1{N}_1=T_2{N}_2=Constant$.

Hence $T_1=20,N_1=4$ and $N_2=5$, $T_2=?$. Therefore $T_1{N}_1=T_2{N}_2$ or $T_2=\frac{T_1{N}_1}{N_2}=\frac{4\times 20}{5}=16days$. Hence $T_1-T_2=20-16=4days$.