The number of tables that can be purchased by a person in Rs.2800 gets reduced by 20 if the price is increased by 40% What is the intial price of each table ?

Options

A. A)Rs. 40
B. B)Rs.36
C. C)Rs. 48
D. D)Rs. 56

Answer

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

### Step 1: Define Variables
Let the initial price of each table be \( P \) (in Rs).

### Step 2: Determine the Number of Tables
The number of tables that can be purchased with Rs. 2800 at the initial price \( P \) is given by:
\[ \text{Number of tables} = \frac{2800}{P} \]

### Step 3: Calculate the Increased Price
If the price of each table is increased by 40%, the new price \( P' \) is:
\[ P' = P + 0.4P = 1.4P \]

### Step 4: Determine the New Number of Tables
The number of tables that can be purchased at the new price \( P' \) is:
\[ \text{New number of tables} = \frac{2800}{1.4P} \]

### Step 5: Set Up the Equation
According to the problem, the number of tables purchased decreases by 20 when the price is increased. Therefore, we can set up the equation:
\[ \frac{2800}{P} - \frac{2800}{1.4P} = 20 \]

### Step 6: Simplify the Equation
To simplify the left side of the equation, we can find a common denominator:
\[ \frac{2800 \cdot 1.4 - 2800}{1.4P} = 20 \]
\[ \frac{2800 \cdot 0.4}{1.4P} = 20 \]

### Step 7: Solve for \( P \)
Now, we can simplify further:
\[ \frac{1120}{1.4P} = 20 \]
Multiplying both sides by \( 1.4P \):
\[ 1120 = 20 \cdot 1.4P \]
\[ 1120 = 28P \]
Now, divide both sides by 28:
\[ P = \frac{1120}{28} = 40 \]

### Conclusion
The initial price of each table is Rs. 40.