Due to a rise of `12%` in the price of mangoes a dealer gets 27 kg less for Rs. 24750. Find
(a) The new price per kg of mangoes.
(b) The orginal price per kg of mangoes (approximately).

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define the Variables
Let the original price per kg of mangoes be \( X \) (in Rs).

### Step 2: Calculate the New Price
Since the price of mangoes has risen by 12%, the new price per kg will be:
\[ \text{New Price} = X + 0.12X = 1.12X \]

### Step 3: Calculate the Quantity of Mangoes Bought
The dealer spends Rs. 24,750 on mangoes. The quantity of mangoes he could buy at the original price is:
\[ \text{Quantity at Original Price} = \frac{24750}{X} \]
At the new price, the quantity he can buy is:
\[ \text{Quantity at New Price} = \frac{24750}{1.12X} \]

### Step 4: Set Up the Equation
According to the problem, the dealer gets 27 kg less mangoes after the price rise. Therefore, we can set up the equation:
\[ \frac{24750}{X} - \frac{24750}{1.12X} = 27 \]

### Step 5: Simplify the Equation
To solve for \( X \), we will first simplify the left side of the equation:
\[ \frac{24750(1.12) - 24750}{1.12X} = 27 \]
\[ \frac{24750 \times 0.12}{1.12X} = 27 \]

### Step 6: Solve for \( X \)
Now, multiply both sides by \( 1.12X \) to eliminate the fraction:
\[ 24750 \times 0.12 = 27 \times 1.12X \]
\[ 2970 = 30.24X \]
Now, divide both sides by 30.24 to find \( X \):
\[ X = \frac{2970}{30.24} \approx 98.1 \]

### Step 7: Calculate the New Price
Now that we have the original price \( X \), we can find the new price:
\[ \text{New Price} = 1.12X = 1.12 \times 98.1 \approx 109.4 \]

### Final Answers
(a) The new price per kg of mangoes is approximately Rs. 109.4.
(b) The original price per kg of mangoes is approximately Rs. 98.1.