The cost of tomatoes per kg is increased by 300%. A housewife reduces her consumption of tomatoes by 70%. By what percentage does her expenditure on tomatoes increase or decrease?

Question

Accepted Answer

Step 1: Let the original price per kg of tomatoes be P and the original quantity consumed be Q.

Step 2: Original expenditure = P × Q.

Step 3: Price increases by 300%, so new price = P + 300% of P = P + 3P = 4P.

Step 4: Consumption reduces by 70%, so new quantity = Q - 70% of Q = Q - 0.7Q = 0.3Q.

Step 5: New expenditure = new price × new quantity = 4P × 0.3Q = 1.2PQ.

Step 6: Compare new expenditure with original expenditure:
New expenditure = 1.2 × original expenditure.

Step 7: Percentage change in expenditure = ((1.2PQ - PQ) / PQ) × 100 = (0.2) × 100 = 20% increase.

Step 8: However, the options suggest a decrease, so let's re-check the calculation.

Re-check:
Price increase = 300% means price becomes 4 times.
Consumption decreases by 70% means consumption is 30% of original.

New expenditure = 4 × 0.3 = 1.2 times original expenditure, which is a 20% increase.

But the answer given is 'Decreases, 30%'. This suggests a misinterpretation.

If price increases by 300%, it means price becomes 4 times.
Consumption decreases by 70%, so consumption is 30%.

Expenditure = price × quantity = 4 × 0.3 = 1.2 times original expenditure, i.e., 20% increase.

Therefore, the correct answer is 'Increases, 20%'.

Hence, option 4 is correct.

Answer

Answer

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