# The ratio of the price of two bicycles was 7 : 8. Two years later, when the price of the first has risen by 30% and the price of the second increases

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The ratio of the price of two bicycles was 7 : 8. Two years later, when the price of the first has risen by 30% and the price of the second increases by Rs. 1,500, then their prices are in the ratio 15 : 16. What is the original price of (in Rs.) the second bicycle?
1. 7,031.25
2. 8,103.25
3. 7,013.25
4. 8,031.25

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Correct Answer - Option 1 : 7,031.25

Given:

The ratio of the price of two bicycles was 7 : 8.

The price of the first has risen by 30%.

The price of the second increases by Rs.1,500.

The final ratio of their prices is 15 : 16.

Concept Used:

The increased value = (100 + percentage)/100 × Initial value

Calculation:

Let the price of first cycle be 7x.

Let the price of second cycle be 8x.

After 2 years, the price of first cycle = (100 + 30)/100 × 7x = 9.1x

After 2 years, the price of second cycle = 8x + 1500

According to the question;

The final ratio of their prices is 15 : 16.

⇒ 9.1x/(8x + 1500) = 15/16

⇒ 145.6x = 120x + 22500

⇒ 25.6x = 22500

⇒ x = 22500/25.6 = 5625/6.4

The price of second cycle = 8x = 8 × 5625/6.4 = Rs.7031.25

∴ The price of second cycle is Rs.7031.25.