Akbar and Birbal who purchased the shares for the cost of their basic salaries which are in the ratio of 5 :6. later on company gave them 40 additional shares to each, due to which the ratio changed to 7 : 8. If the worth of each share is ₹ 75, what is the basic salary of the person who got less shares?

Options

A. ₹ 10500
B. ₹ 7500
C. ₹ 8800
D. ₹ 9000

Answer

To solve the problem step by step, we will follow the given information and derive the necessary equations to find the basic salary of Akbar, who received fewer shares.

### Step 1: Define the Basic Salaries
Let the basic salaries of Akbar and Birbal be represented as:
- Akbar's salary = 5k
- Birbal's salary = 6k

### Step 2: Calculate the Initial Investment in Shares
Since they purchased shares with their salaries, the total amount spent on shares can be calculated as:
- Cost of Akbar's shares = 5k
- Cost of Birbal's shares = 6k

### Step 3: Determine the Number of Shares Purchased
The worth of each share is given as ₹75. Therefore, the number of shares they could buy initially would be:
- Number of shares Akbar bought = (5k) / 75
- Number of shares Birbal bought = (6k) / 75

### Step 4: Add the Additional Shares
Both Akbar and Birbal received 40 additional shares:
- New number of shares for Akbar = (5k / 75) + 40
- New number of shares for Birbal = (6k / 75) + 40

### Step 5: Set Up the New Ratio
After receiving the additional shares, the new ratio of their shares is given as 7:8. Therefore, we can write the equation:
\[ \frac{(5k / 75) + 40}{(6k / 75) + 40} = \frac{7}{8} \]

### Step 6: Cross Multiply to Solve for k
Cross-multiplying gives us:
\[ 8 \left( \frac{5k}{75} + 40 \right) = 7 \left( \frac{6k}{75} + 40 \right) \]

Expanding both sides:
\[ \frac{40k}{75} + 320 = \frac{42k}{75} + 280 \]

### Step 7: Rearranging the Equation
Rearranging the equation to isolate k:
\[ 40k - 42k = 280 - 320 \]
\[ -2k = -40 \]
\[ k = 20 \]

### Step 8: Calculate Akbar's Basic Salary
Now that we have the value of k, we can find Akbar's basic salary:
\[ \text{Akbar's salary} = 5k = 5 \times 20 = ₹100 \]

### Step 9: Calculate Birbal's Basic Salary
To confirm, we can also calculate Birbal's basic salary:
\[ \text{Birbal's salary} = 6k = 6 \times 20 = ₹120 \]

### Conclusion
Since Akbar received fewer shares, his basic salary is ₹100.