An increase of 25 percent in the price of onions enables a woman to buy 5 kg less for Rs. 200. The increased price of onions per kg is:

Correct option is C

Given:

The woman spends Rs. 200 to buy onions.

Due to a 25% price increase, she buys 5 kg less onions.

Solution:

The initial price per kg of onions = X Rs.

The initial quantity bought = $$\frac{200}{X} \text{ kg}$$​​

The new price = 1.25X  Rs/kg

So, the new quantity bought = $$\frac{200}{1.25X} \text{ kg}$$​​

Equating the difference to 5 kg:

​$$\frac{200}{X} - \frac{200}{1.25X} = 5 \\ \ \\200 - 160 = 5X \\ \ \\40 = 5X \\ \ \\ X = 8 \text{ Rs/kg (Initial price)}$$​​

The increased price = $$1.25 \times 8$$​ = 10  Rs/kg 

Alternate Solution: ​

Consumption $$\propto$$ $$\frac{1}{Price}$$ 

Price = 25% increase

Price ratio :                  4      :      5 

Consumption ratio:     5      :      4 

Decrease in consumption = 5 - 4 = 1 

1 unit = 5 kg 

4 unit = 20 kg  

New price = $$\frac{200}{20} = 10\ Rs/kg$$​​