Question

Raman bought two watches. He later realised that he actually needs none of the watches. So, he sold them for 7600 each, making a loss of 20% on one and gain of 20% on the other. Did he make a profit on the whole transaction or a loss? And how much? ​

Answer 1

Let's analyze the situation step by step:

• Raman bought two watches.
• He sold the first watch at a loss of 20%.
• He sold the second watch at a gain of 20%.

Let's assume the cost price of both watches was the same, let's say "C".

For the first watch:

• He sold it for 7600, which is 80% of its cost price (since he made a loss of 20%).
• So, 80% of C = 7600.
• C = 7600 / 0.8 = 9500.

For the second watch:

• He sold it for 7600, which is 120% of its cost price (since he made a gain of 20%).

• So, 120% of C = 7600.
• C = 7600 / 1.2 = 6333.33.

Now, let's calculate the total cost price (C) and the total selling price (S):

• Total cost price = 9500 + 6333.33 = 15833.33.
• Total selling price = 7600 + 7600 = 15200.

• Total Loss or Gain = Total Selling Price - Total Cost Price
• Total Loss or Gain = 15200 - 15833.33 = -633.33.

Raman made a loss of 633.33 on the whole transaction.

Answer 2

633.33

Explanation:

1. Let's assume the cost price of the first watch is x. - Raman sold this watch at a 20% loss, which means he sold it for 80% of its cost price.

- Therefore, he sold the first watch for 0.8x.

2. The cost price of the second watch is y. - Raman sold this watch at a 20% gain, which means he sold it for 120% of its cost price.

- Therefore, he sold the second watch for 1.2y.

3. Raman sold each watch for 7600, so we can set up the following equations:

- 0.8x = 7600 - 1.2y = 7600

4. Solving these equations will give us the values of x and y. - From the first equation, we find that x = 7600 / 0.8 = 9500. - From the second equation, we find that y = 7600 / 1.2 = 6333.33 (rounded to two decimal places).

5. Now, let's calculate the total cost price of both watches: - Total cost price = x + y = 9500 + 6333.33 = 15833.33 (rounded to two decimal places).

6. Next, let's calculate the total selling price of both watches: - Total selling price = 7600 + 7600 = 15200.

7. To determine if Raman made a profit or a loss, we compare the total cost price with the total selling price:

- If the total selling price is greater than the total cost price, Raman made a profit.

- If the total selling price is less than the total cost price, Raman made a loss.

8. In this case, the total selling price (15200) is less than the total cost price (15833.33), which means Raman made a loss on the whole transaction.

9. To calculate the amount of loss, we subtract the total selling price from the total cost price: - Loss = Total cost price - Total selling price = 15833.33 - 15200 = 633.33 (rounded to two decimal places).

Therefore, Raman made a loss of approximately 633.33 in the whole transaction.