Due to 10% reduction in the price of sugar a person can buy 5 kg more sugar for ₹ 300. Find the reduction in the price of sugar per kg.

Correct option is A

Given:

Reduction in price = 10%

Increased quantity = 5 kg

Total money spent = ₹300

Solution:

Let the original price of sugar be ₹x per kg.
Then, the quantity of sugar bought at the original price:​$$\frac{300}{x}$$​

After a 10% reduction, the new price per kg:​$$\frac{90}{100} \times x = \frac{9}{10}x$$​

The new quantity of sugar bought = $$\frac{300 \times 10}{9x}$$​​

$$\frac{3000}{9x} - \frac{300}{x} = 5$$​

$$\frac{3000}{9x} - \frac{2700}{9x} = 5\\\frac{300}{9x} = 5\\300 = 5 \times 9x\\300 = 45x\\x = \frac{300}{45} = \frac{20}{3}\\$$

Reduced Price =  $$\frac{9}{10}x = \frac{9}{10} \times \frac {20}3 = 6$$ 
Alternate Solution:

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

10% = $$\frac{1}{10}$$

Price                                10      :          9

Consumption                   9          :         10 

1 unit = 5 kg  
So, Final Purchase Quantity = R. 50 per kg

Final price = $$\frac{300}{50}$$ = 6 

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