Rajat sells a toy for Rs 650 gaining 1/5 of its cost price. Find his gain %.

Let the cost price of the toy be \( C \).

Rajat gains \( \frac{1}{5} \) of the cost price, which means his gain is:
\[
\text{Gain} = \frac{C}{5}
\]

The selling price \( S \) is given as Rs 650. The selling price is the sum of the cost price and the gain:
\[
S = C + \frac{C}{5}
\]

Substituting \( S = 650 \) into the equation:
\[
650 = C + \frac{C}{5}
\]

To simplify, multiply the entire equation by 5 to eliminate the fraction:
\[
5 \times 650 = 5 \times C + C
\]
\[
3250 = 6C
\]

Now solve for \( C \):
\[
C = \frac{3250}{6} = 541.67 \, \text{Rs}
\]

Now that we know the cost price, we can calculate the gain:
\[
\text{Gain} = 650 - 541.67 = 108.33 \, \text{Rs}
\]

Finally, the gain percentage is given by:
\[
\text{Gain \%} = \left( \frac{\text{Gain}}{C} \right) \times 100 = \left( \frac{108.33}{541.67} \right) \times 100 \approx 20\%
\]

Thus, Rajat's gain percentage is **20%**.

Would you like more details on any step or have any questions?

Here are 5 related questions for further practice:
1. If the cost price was Rs 800 and Rajat still gained 1/5 of the cost price, what would be the selling price?
2. If Rajat made a gain of 25% instead of 1/5, what would be the new selling price for the toy?
3. How would the gain percentage change if Rajat sold the toy for Rs 700?
4. If the selling price was Rs 750 and the gain percentage was 10%, what was the cost price?
5. What is the loss percentage if the toy was sold for Rs 500 instead of Rs 650?

**Tip:** To quickly calculate percentages, remember that percentages are fractions of 100, and multiplying by 100 helps express a value as a percentage.

Learn how to calculate the gain percentage when Rajat sells a toy for Rs 650, making a gain of 1/5 of its cost price. This step-by-step solution includes key profit and percentage formulas. Suitable for students in Grades 6-8.

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