If the price of sugar decreases by 10%, a man enable to purchase 5 kg more sugar in Rs.450. Find the original price of sugar. 

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  1. Rs.15 per kg
  2. Rs.10 per kg
  3. Rs.11 per kg
  4. Rs.12 per kg

Answer (Detailed Solution Below)

Option 2 : Rs.10 per kg
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Detailed Solution

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Given:

Decrease in price = 10%

Additional sugar purchased = 5 kg

Total amount spent = ₹450

Formula used:

Original price per kg = (Total amount ÷ (Quantity before decrease))

New price per kg = Original price per kg × (1 - 10/100)

Calculation:

Let original price per kg = x

Quantity before decrease = 450 ÷ x

Quantity after decrease = 450 ÷ (x × 0.9)

⇒ 450 ÷ (0.9x) - 450 ÷ x = 5

⇒ (450 - 450 × 0.9) ÷ (0.9x) = 5

⇒ (450 × 0.1) ÷ (0.9x) = 5

⇒ 45 ÷ (0.9x) = 5

⇒ 45 = 5 × 0.9x

⇒ 45 = 4.5x

⇒ x = 45 ÷ 4.5

⇒ x = 10

∴ The original price of sugar is ₹10 per kg.

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