Question : If 540 kg of grass would feed 100 cows for 9 days, then for how many days would 900 kg of grass feed 50 cows?
Option 1: 50 days
Option 2: 10 days
Option 3: 20 days
Option 4: 30 days
Correct Answer: 30 days
Solution :
$M_1$ = 100, $D_1$ = 9 days, $W_1$ = 540 kg
$M_2$ = 50, $W_2$ = 900 kg
where $M_1, M_2$ are numbers of cows, $D_1, D_2$ are days, and $W_1, W_2$ are weight of grass.
We know, $\frac{M_1 × D_1}{W_1}$ = $\frac{M_2 × D_2}{W_2}$
⇒ $\frac{100 × 9}{540}$ = $\frac{50 × D_2}{900}$
$\therefore D_2$ = $\frac{100 × 9 × 900}{540 × 50}$ = 30 days
Hence, the correct answer is 30 days.
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