Question

If 20 cows graze 2 fields in 10 days, then how many fields will be grazed by 40 cows in 8 days?

• A. $3\frac{1}{5}\text{fields.}$
• B. $3\text{fields}$
• C. $3\frac{2}{5}\text{fields}$
• D. $4\text{fields}$

Answer 1

The correct option is A $3\frac{1}{5}\text{fields.}$

Here, the number of fields grazed is directly proportional to the number of days and also directly proportional to the number of cows.

Number of fields grazed	Number of days	Number of cows
2	10	20
$x$	8	40
2: $x$	10:8 = 5:4	20:40 = 1:2

Number of fields grazed $\propto$ Number of days
$\Rightarrow 2:x=5:4$...(i)

Number of fields grazed $\propto$ Number of cows
$\Rightarrow 2:x=1:2$...(ii)

From (i) and (ii)
2 : $x$
$=\text{compound ratio of}5:4\text{and}1:2$
$\Rightarrow 2:x=(5:4)\times (1:2)$
$\Rightarrow 2:x=(5\times 1):(4\times 2)$
$\Rightarrow 2:x=(5:8)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 5=2\times 8$
$\Rightarrow x=\frac{16}{5}=3\frac{1}{5}fields$

So, in 8 days, 40 cows will graze
$3\frac{1}{5}\text{fields.}$