If due to 10% decrease in the price of sugar, Ram can buy 5 kg more sugar in ₹ 100 , then the actual price of the sugar (in ₹) per kg is

Correct option is B

Given:
Decrease in price = 10%
Extra quantity = 5 kg
Total expenditure = ₹100
Formula Used:
Quantity = $$\frac{Expenditure}{Price}$$​​
Solution:
Let the original actual price of sugar be P per kg.
The new reduced price = P - 10% of P = 0.9P.
According to the question, the difference in quantities bought at the new price and old price is 5 kg.
​$$\frac{100}{0.9P} - \frac{100}{P} = 5$$​​
​$$\frac{100}{P} × (\frac{1}{0.9} - 1) = 5\\ \ \\\frac{100}{P} × (\frac{10}{9} - 1) = 5\\ \ \\\frac{100}{P} × \frac{1}{9} = 5\\ \ \\\frac{100}{9P} = 5\\ \ \\45P = 100 \\ \ \\P = \frac{100}{45} = \frac{20}{9}$$​​
Converting the improper fraction to a mixed fraction, P = $$2 \frac{2}{9}$$​​
Final Answer
So the correct answer is (b)