Two friends bought two bicycles whose prices were in the ratio of 1:5. If they sold them at a loss of 10%, the difference of the money earned by them was Rs. 3600. What was the cost of the costlier cycle?


Question 20Answer

a. 

4000

b. 

5000

c. 

7000

d. 

None

Let the cost of the cheaper bicycle be \( x \). Then, the cost of the costlier bicycle is \( 5x \) since the ratio of their prices is 1:5.

Now, both bicycles are sold at a 10% loss. Therefore, the selling price of the cheaper bicycle is:

\[
\text{Selling price of cheaper bicycle} = x - 0.1x = 0.9x
\]

Similarly, the selling price of the costlier bicycle is:

\[
\text{Selling price of costlier bicycle} = 5x - 0.1(5x) = 0.9(5x) = 4.5x
\]

According to the problem, the difference in the money earned by them is Rs. 3600:

\[
4.5x - 0.9x = 3600
\]

Simplifying the left-hand side:

\[
3.6x = 3600
\]

Solving for \( x \):

\[
x = \frac{3600}{3.6} = 1000
\]

Thus, the cost of the costlier bicycle is \( 5x = 5 \times 1000 = 5000 \).

So, the correct answer is:

**b. 5000**

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the solution change if the loss percentage was different, say 15%?
2. What would the cost of the cheaper bicycle be in this case?
3. How does the concept of ratios help in solving real-world problems?
4. Can you derive the formula for percentage loss or gain in general?
5. How would you handle the problem if there were more than two friends and bikes?

**Tip:** Always verify your final answer by plugging the values back into the original equation to check for consistency.

Two friends bought two bicycles whose prices were in the ratio of 1:5. If they sold them at a loss of 10%, the difference of the money earned by them was Rs. 3600. What was the cost of the costlier cycle?

Learn how to calculate the cost of a bicycle given that two friends bought bicycles with prices in the ratio of 1:5 and sold them at a 10% loss. This problem uses key mathematical concepts like ratios, percentage loss, and linear equations. Suitable for students in Grades 8-10.

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