Question

The price of an apple is twice that of an orange. The price of an orange is thrice that of a banana. If the price of an apple increases by 10%, price of an orange increases by 30% and the price of a banana increases by 20%. Find the percentage increase in the price of 20 apples, 20 oranges and 20 bananas.

• A. 19%
• B. 17%
• C. 15%
• D. 13%

Answer 1

The Correct Option is B

To find the percentage increase in the price of 20 apples, 20 oranges, and 20 bananas, we first need to understand the relationship in their initial prices and the effect of the given price increases.

1. Assume the initial price of a banana = \(B\).
2. The price of an orange is thrice that of a banana, so: \(O = 3B\)
3. The price of an apple is twice that of an orange, so: \(A = 2 \times 3B = 6B\)
4. Calculate the total price before the increase: \(20A + 20O + 20B = 20(6B) + 20(3B) + 20B = 120B + 60B + 20B = 200B\)
5. After the price increases:
   • The price of an apple increases by 10% to \(6B \times 1.10 = 6.6B\)
   • The price of an orange increases by 30% to \(3B \times 1.30 = 3.9B\)
   • The price of a banana increases by 20% to \(B \times 1.20 = 1.2B\)
6. Calculate the new total price after the increase: \(20(6.6B) + 20(3.9B) + 20(1.2B) = 132B + 78B + 24B = 234B\)
7. Determine the increase in total price: \(234B - 200B = 34B\)
8. Calculate the percentage increase: \(\left( \frac{34B}{200B} \right) \times 100\% = 17\%\)

Thus, the percentage increase in the price of 20 apples, 20 oranges, and 20 bananas is 17%.

The correct answer is: 17%.