The price of petrol is increased by `30%` then a man can purchase 9lt.less petrol for 780. Find original price of petrol

Options

A. 39ltr,30ltr,20Rs./ltr,26 Rs./ltr
B. 35ltr,26ltr,20Rs./ltr,22 Rs./ltr
C. 39ltr,30ltr,30Rs./ltr,36 Rs./ltr
D. 29ltr,30ltr,30Rs./ltr,26 Rs./ltr

Answer

To solve the problem step-by-step, we can follow these steps:

### Step 1: Define the original price of petrol
Let the original price of petrol be \( X \) (in rupees per liter).

### Step 2: Calculate the increased price of petrol
The price of petrol is increased by 30%. Therefore, the new price of petrol will be:
\[ \text{New Price} = X + 0.30X = 1.3X \]

### Step 3: Determine the quantity of petrol purchased before and after the price increase
If a man spends ₹780 on petrol at the original price \( X \), the quantity of petrol he can buy is:
\[ \text{Quantity at original price} = \frac{780}{X} \text{ liters} \]

After the price increase, the quantity of petrol he can buy is:
\[ \text{Quantity at increased price} = \frac{780}{1.3X} \text{ liters} \]

### Step 4: Set up the equation based on the problem statement
According to the problem, the man can purchase 9 liters less petrol after the price increase. Therefore, we can set up the equation:
\[ \frac{780}{X} - \frac{780}{1.3X} = 9 \]

### Step 5: Simplify the equation
To simplify the equation, first find a common denominator:
\[ \frac{780 \cdot 1.3 - 780}{1.3X} = 9 \]
This simplifies to:
\[ \frac{780(1.3 - 1)}{1.3X} = 9 \]
\[ \frac{780 \cdot 0.3}{1.3X} = 9 \]

### Step 6: Multiply both sides by \( 1.3X \)
\[ 780 \cdot 0.3 = 9 \cdot 1.3X \]
\[ 234 = 11.7X \]

### Step 7: Solve for \( X \)
Now divide both sides by 11.7:
\[ X = \frac{234}{11.7} \]
Calculating this gives:
\[ X = 20 \]

### Conclusion
The original price of petrol is \( \text{₹} 20 \).

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