Every month a man consumes 25 kg rice and 9 kg wheat. The price of rice is 20% of the price of wheat and thus he spends total Rs. 350 on the rice and wheat per month. If the price of wheat is increased by 20% then what is the percentage reduction of rice consumption for the same expenditure of Rs. 350? (Given that the price of rice and consumption of wheat is constant)

(a) 36%

(b) 25%

(c) 40%

(d) 24%

**Ans**: (a) 36%

**Explanation**:

Let, Rice = 25 kg at ₹ x/kg

and wheat = 9 kg at ₹ 5x/kg

∴ 25x + 45x = 350

⇒ 70x = 350

⇒ x = 5

Hence, price of rice per kg = 5

and price of wheat per kg = 25

For new case,

Rice = y kg at ₹ 5/kg

Wheat = 9 kg at 25 × \displaystyle\frac{6}{5} = ₹ 30/kg

∴ 5y + 270 = 350

⇒ y = 16

Consumption of rice reduced from 25 kg to 16 kg.

Hence, reduction in consumption of rice

= \displaystyle\frac{25-16}{25} × 100 = 36%

**Aliter(Ratio Method)**

Hence, reduction in consumption of rice

= \displaystyle\frac{25-16}{25} × 100 = 36%

**Explanation**:

From the question we have understood that expenditure remain same.

Initial expenditure = 25 × 1 + 9 × 5 = 70

So, final expenditure will also be 70

Later expenditure on wheat = ₹ 54

So, rice will take = 70 – 54 = ₹ 16

Price of rice is still ₹ 1/kg

So, consumption of rice will be 16 kg

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