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:

20\% = \displaystyle\frac{1}{5}

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%