Ritesh bought 2 kg less onions in 155 due to an increase in price of onions by 12%. What increased price of onions per kg? Also find the original price of unions

To solve this problem, let's define the variables:

- Let \( x \) be the original price of onions per kg.
- Let \( y \) be the original quantity of onions Ritesh could buy for ₹155.
- The increased price of onions per kg would then be \( x + 0.12x = 1.12x \).

Given:
1. Ritesh bought 2 kg less onions after the price increased by 12%.
2. The total expenditure remained the same, ₹155.

First, calculate the original quantity of onions \( y \):
\[ y = \frac{155}{x} \]

After the price increase, the quantity of onions he could buy is \( y - 2 \):
\[ y - 2 = \frac{155}{1.12x} \]

Now, substitute the expression for \( y \) from the first equation into the second equation:
\[ \frac{155}{x} - 2 = \frac{155}{1.12x} \]

To solve for \( x \), follow these steps:

1. Multiply both sides of the equation by \( 1.12x \) to clear the denominators:
\[ 1.12x \left( \frac{155}{x} - 2 \right) = 155 \]

2. Distribute \( 1.12x \) on the left side:
\[ 1.12 \cdot 155 - 2 \cdot 1.12x = 155 \]

3. Simplify the constants:
\[ 173.6 - 2.24x = 155 \]

4. Isolate \( x \) by subtracting 155 from both sides:
\[ 173.6 - 155 = 2.24x \]
\[ 18.6 = 2.24x \]

5. Divide both sides by 2.24:
\[ x = \frac{18.6}{2.24} \]
\[ x \approx 8.3036 \]

So, the original price of onions per kg was approximately ₹8.30.

To find the increased price:
\[ 1.12x = 1.12 \times 8.3036 \]
\[ 1.12x \approx 9.30 \]

Therefore, the increased price of onions per kg is approximately ₹9.30.

### Summary:
- **Original price of onions per kg:** ₹8.30
- **Increased price of onions per kg:** ₹9.30

Would you like details or have any questions?

Here are 8 related questions to expand your understanding:

1. How does a percentage increase affect the overall cost?
2. What other factors could cause the price of onions to rise?
3. How would you calculate the new price if the increase was 15% instead of 12%?
4. How do you solve similar problems involving percentage decreases?
5. What if the expenditure changed instead of the price? How would that affect the solution?
6. Can you generalize this method for any percentage increase and expenditure amount?
7. How do different pricing strategies affect consumer behavior?
8. What mathematical tools are useful for handling percentage-related problems?

**Tip:** Always double-check your calculations for accuracy, especially when dealing with percentages and unit conversions.

Learn how to calculate the increased price of onions per kg after a 12% rise, given the original price was ₹8.30 per kg. This math problem involves calculating unit price, percentage increase, and maintaining a fixed expenditure. Suitable for high school students and anyone interested in price calculations.

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