Question

A reduction of Rs.2 /kg enables a man to purchase a 4 kg more sugar for Rs.16. Find the original price of sugar?

• A. Rs.4
• B. Rs.8
• C. Rs.3
• D. Rs.5

Answer 1

The correct option is A Rs.4

Let the total price of sugar be Rs x

The total price of an entity = (Quantity of entity) X (Price of single entity)

Similarly, the Quantity of sugar $=\frac{\text{Total price of sugar}}{\text{price of 1 kg sugar}}$

Quantity of sugar before price reduction $=\frac{16}{x}$

Quantity of sugar after price reduction $=\frac{16}{x-2}$

Also new quantity of sugar after price reduction is 4 kg more than the initial quantity.

$\Rightarrow \frac{16}{x-2}=\frac{16}{x}+4\Rightarrow \frac{16}{x-2}-\frac{16}{x}=4\Rightarrow \frac{16(x-x+2)}{x(x-2)}=4\Rightarrow x(x-2)=8\Rightarrow x^2-2x-8=0\Rightarrow x^2-4x+2x-8=0\Rightarrow x(x-4)+2(x-4)=0\Rightarrow (x-4)(x-2)=0\Rightarrow x=4orx=-2$

Quantity can't be negative

$\therefore x=4$ [ original price of sugar ]

option A is correct answer.