Question

The cost of 12 quintals of soybean is 36000 rupees. How much will 8 quintals cost?

Answer 1

Hint: Assume that the cost of 8 quintals of soybean is x. Use the fact that the ratio of cost to the amount of soybean should be constant and hence prove that $x:8::36000:12$. Use the fact that in a proportion the product of means is equal to the product of extremes and hence form an equation in x. Solve for x and hence find the cost of 8 quintals of soybean. Alternatively, find the cost of 1 quintal of soybean and hence calculate the cost of 8 quintals of soybean.

Complete step-by-step answer:
Let the cost of 8 quintals of soybean be x.
Since we know that the ratio of cost to amount should be constant, we have
$x:8::36000:12$
We know that in a proportion product of means is equal to the product of extremes, i.e. if a:b::c:d then ad = bc
Here extremes are x and 12, and the means are 8 and 36000
Hence, we have
$12x=8\times 36000$
Dividing both sides by 12, we get
$x=\dfrac{36000\times 8}{12}=24000$
Hence the cost of 8 quintals of soybean is Rs. 24000

Note: Alternative Solution: Unitary method:
Cost of 12 quintals of soybean = Rs. 36000
Hence, we have
The cost of 1 quintal of soybean $=\dfrac{36000}{12}=3000$
Hence the cost of 1 quintal of soybean is Rs. 3000
Hence the cost of 8 quintals of soybean is $3000\times 8=24000$
Hence the cost of 8 quintals of soybean is Rs 24000, which is the same as obtained above.