Bicycle Prices Ratio Calculation

Let the initial prices of the two bicycles be $15x$ and $26x$, according to the given ratio of 15:26.

New Prices After Changes

The price of the first bicycle is increased by 10%. New price of the first bicycle = $15x + (10\% \text{ of } 15x)$ New price of the first bicycle = $15x + (0.10 \times 15x)$ New price of the first bicycle = $15x + 1.5x = 16.5x$

The price of the second bicycle is increased by Rs. 550. New price of the second bicycle = $26x + 550$

Setting Up the New Ratio Equation

The new ratio between the prices is given as 13:22. Therefore, we can write the equation: $ \frac{16.5x}{26x + 550} = \frac{13}{22} $

Solving for the Variable 'x'

Cross-multiply the terms: $ 22 \times 16.5x = 13 \times (26x + 550) $ $ 363x = 338x + 13 \times 550 $ $ 363x = 338x + 7150 $ Subtract $338x$ from both sides: $ 363x - 338x = 7150 $ $ 25x = 7150 $ Solve for $x$: $ x = \frac{7150}{25} $ $ x = 286 $

Calculating Initial Bicycle Prices

Now, substitute the value of $x$ back into the expressions for the initial prices.

• Initial price of the first bicycle = $15x = 15 \times 286 = 4290$
• Initial price of the second bicycle = $26x = 26 \times 286 = 7436$

So, the initial prices were Rs. 4290 and Rs. 7436.