Question

Rice is now being sold at Rs. 29 per kg. During the last month, its cost was Rs. 25 per kg. By how much percentage should a family reduce its consumption, so as to keep the expenditure the same as before?

(correct to nearest integer)

1. 13%
2. 15%
3. 14%
4. 12%

Answer 1

Correct Answer - Option 3 : 14%

Given:

New selling price = Rs. 29 per kg

Old selling price = Rs. 25 per kg

Expenditure = constant

Formula used:

(i) Expenditure = Price × Quantity

(ii) Percentage difference = {(Old price - New price)/Old price} × 100

Calculations:

Let expenditure, initial selling price and initial quantity be C, P₁ and Q₁ respectively.

C = P₁ × Q₁

⇒ C = 25 × Q₁

⇒ Q₁ = C/25

Let final selling price and final quantity be P₂ and Q₂ respectively.

C = P₂ × Q₂

⇒ C = 29 × Q₂

⇒ Q₂ = C/29

Percentage difference = (Q₂ - Q₁)/Q₁ ×100

⇒ {(C/29 - C/25)/(C/25)} ×100

⇒ [{(25C - 29C)/(25 × 29)}/(C/25)] × 100

⇒ {–(4C/725)/(C/25)} × 100

⇒ {–(4C × 25)/725C} × 100

⇒ –13.79% ≈ –14%

∴ By 14% should a family reduce its consumption, so as to keep the expenditure the same as before.