Question

Reduction of rupees 2 per kg enables a man to purchase 4 kg more sugar for 16 rupees find the original price of sugar

Answer 1

let the orriginal price of sugar be Rs x per kg

quantity purchased is 16/x kg.

after reducing quantity purchased = 16/x - 2kg

 ⇒16/x - 2 = 16/x + 4 

⇒ x = 4

Answer 2

The original price of sugar is 4 rupees.

Solution:

Let the original price of Sugar be x rupees.

$\text {Total price of any entity} =\text {Quantity of entity} \times \text {Price of single entity}$

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

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 kgs more than the initial quantity.

$\Rightarrow \frac{16}{x-2}=\frac{16}{x}+4$

$\Rightarrow \frac{16}{x-2}-\frac{16}{x}=4$

$\Rightarrow \frac{16(x-x+2)}{x(x-2)}=4$

$\Rightarrow x(x-2)=8$

$\Rightarrow x^{2}-2 x-8=0$

$\Rightarrow x^{2}-4 x+2 x-8=0$

$\Rightarrow x(x-4)+2(x-4)=0$

$\Rightarrow(x-4)(x+2)=0$

$\Rightarrow x=4 \text { or } x=-2$

Therefore, x = 4 quantity cannot be negative.