The total salary of Gaurav and Azam in a company is Rs.47520. If the salary of Gaurav increases by 23% and Azam increases by 30% then their total salary would increase to Rs.59928. Find the difference between their salary?

Options

A. Rs. 5280
B. Rs.4720
C. Rs.6290
D. Rs.8428

Answer

To solve the problem step by step, let's denote Gaurav's salary as \( G \) and Azam's salary as \( A \). We know the following:

1. The total salary of Gaurav and Azam is given as:
\[ G + A = 47520 \]

2. After the salary increases, Gaurav's salary increases by 23% and Azam's salary increases by 30%. The new total salary is:
\[ G \times 1.23 + A \times 1.30 = 59928 \]

Now, we can set up the equations based on the information provided.

### Step 1: Express Azam's salary in terms of Gaurav's salary
From the first equation:
\[ A = 47520 - G \]

### Step 2: Substitute Azam's salary into the second equation
Substituting \( A \) in the second equation gives:
\[ 1.23G + 1.30(47520 - G) = 59928 \]

### Step 3: Expand and simplify the equation
Expanding the equation:
\[ 1.23G + 1.30 \times 47520 - 1.30G = 59928 \]
Calculating \( 1.30 \times 47520 \):
\[ 1.30 \times 47520 = 61776 \]
Now substituting this back into the equation:
\[ 1.23G - 1.30G + 61776 = 59928 \]
Combining like terms:
\[ -0.07G + 61776 = 59928 \]

### Step 4: Isolate Gaurav's salary
Subtract \( 61776 \) from both sides:
\[ -0.07G = 59928 - 61776 \]
Calculating the right side:
\[ 59928 - 61776 = -1848 \]
So we have:
\[ -0.07G = -1848 \]

### Step 5: Solve for Gaurav's salary
Dividing both sides by \(-0.07\):
\[ G = \frac{-1848}{-0.07} = 26400 \]

### Step 6: Calculate Azam's salary
Now substituting \( G \) back into the equation for \( A \):
\[ A = 47520 - 26400 = 21120 \]

### Step 7: Find the difference between their salaries
Now, we find the difference between Gaurav's and Azam's salaries:
\[ \text{Difference} = G - A = 26400 - 21120 = 5280 \]

Thus, the difference between their salaries is:
\[ \boxed{5280} \]