Question

Due to an decrement of Rs 2 per kg in the price of sugar. A person is able to buy 4 kg more for Rs 16. What is the initial cost of sugar.

Answer 1

Let the cost per kg be x then :

When there is a decrement of rs 2, the selling price is :

(x - 2)

Let the quantity to be bought be y then:

Before decrement :

16/x = y

After decrement :

16/(x - 2) = y + 4

y = 16/(x - 2) - 4

Then equating the two we have :

16/x = 16/(x - 2) - 4

16 = 16x / (x - 2) - 4x

16(x - 2) = 16x - 4x(x - 2)

16x - 32 = 16x - 4x²+8x

4x² - 8x - 32 = 0

Dividing through by 4

x² - 2x - 8 = 0

The roots are 2 and - 4

(x - 4)(x + 2) = 0

x = 4 or - 2

we take the positive value = 4

The initial cost is thus:

rs 4

16/4 = 4 = y

= Rs 4