Question

Fodder costing ₹900 is needed for 15 cows for 10 days. The cost of fodder required for 10 cows for 20 days is .

• A. ₹1,000
• B. ₹1,200
• C. ₹1,400
• D. ₹1,800

Answer 1

The correct option is B ₹1,200

Here, the cost of fodder is directly proportional to the number of cows and directly proportional to the number of days.

Cost of fodder	Number of cows	Number of days
₹900	15	10
$x$	10	20
900:$x$	15:10 = 3:2	10:20 = 1:2

Cost of fodder $\propto$ Number of cows
$\Rightarrow 900:x=3:2$ ...(i)

Cost of fodder $\propto$ Number of days
$\Rightarrow 900:x=1:2$...(ii)

From (i) and (ii)
900 : $x$
$=\text{compound ratio of}3:2\text{and}1:2$
$\Rightarrow 900:x=(3:2)\times (1:2)$
$\Rightarrow 900:x=(3\times 1):(2\times 2)$
$\Rightarrow 900:x=(3:4)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 3=900\times 4$
$\Rightarrow x=₹1,200$

It will cost ₹1,200 to feed 10 cows for 20 days.