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IB ACIO Grade II Previous Paper 13 (Held on: 20 Feb 2021 Shift 3)

Option 4 : 37.5

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__Alternate Method__

**Price × consumption = expenditure **

If price = Rs 1 and consumption is 1 quantity then expenditure is Rs 1.

⇒ 1 × 1 = 1 (using above formula)

Price after increase = 1 + 3/5 × 1 = 8/5 , expenditure = Rs 1 (remains unchanged)

⇒ 8/5 × x = 1

New net use of petrol = 5/8

That is, there is a decrease of = 1 - 5/8 in the consumption of petrol

Percentage decrease = 3/8 × 100 = 37.5%

**Detailed Solution:**

**Given:**

The price of petrol is increased by 60%

**Calculation:**

Let the price of petrol be Rs. 100

If 60% is increased in price = (100 + 60) = Rs. 160

Thus, the reduced consumption for the price to be constant will be,

[(100/100) - (100/160)] × 100

⇒ [1 - (100/ 60)] × 100

⇒ [(160 - 100)/160] × 100

⇒ (60/160) × 100

⇒ (3/8) × 100

⇒ 0.375 × 100

⇒ 37.5 %

**∴ The reduced consumption for the price to be unaffected is 37.5% **

We know that 60% = 3/5

Let the original price of petrol be 5 units

Increased price = 5 + 3 = 8 units

Price is inversely proportional to consumption

Original consumption = 8 units

Increased consumption = 5 units

Consumption in petrol so that expenditure does not fall

⇒ (3/8) × 100 = 37.5%