An Gujrati employee Ramu got promotion, due to this Salary is increased by `26(2)/(3)%`. But due to his inconsistency in work his salary reduced by Rs. 2550. Ramu was transferred to Delhi for a project so his salary is again increased by 12.5%. Now his current salary is Rs. 15300. Find his initial income ?

Options

A. 12750
B. 15750
C. 11250
D. 12000

Answer

To find Ramu's initial income, we will follow these steps:

### Step 1: Define the initial salary
Let the initial salary of Ramu be \( x \).

### Step 2: Calculate the salary after the first increase
Ramu's salary is increased by \( 26 \frac{2}{3} \% \). This can be converted to an improper fraction:
\[ 26 \frac{2}{3} = \frac{80}{3} \% \]
To find the new salary after this increase, we can calculate:
\[ \text{New Salary} = x + \left( \frac{80}{3} \% \text{ of } x \right) = x + \frac{80}{300} \cdot x = x \left( 1 + \frac{80}{300} \right) = x \left( \frac{380}{300} \right) = \frac{19x}{15} \]

### Step 3: Deduct the salary reduction
Ramu's salary is then reduced by Rs. 2550. Therefore, his salary after the deduction becomes:
\[ \text{Salary after deduction} = \frac{19x}{15} - 2550 \]

### Step 4: Calculate the salary after the second increase
Next, Ramu's salary is increased by \( 12.5\% \). This can be expressed as:
\[ 12.5\% = \frac{12.5}{100} = \frac{1}{8} \]
Thus, the new salary after this increase is:
\[ \text{New Salary} = \left( \frac{19x}{15} - 2550 \right) + \left( \frac{1}{8} \text{ of } \left( \frac{19x}{15} - 2550 \right) \right) = \left( \frac{19x}{15} - 2550 \right) \left( 1 + \frac{1}{8} \right) = \left( \frac{19x}{15} - 2550 \right) \left( \frac{9}{8} \right) \]

### Step 5: Set the equation for the current salary
We know that Ramu's current salary is Rs. 15300. Thus, we can set up the equation:
\[ \left( \frac{19x}{15} - 2550 \right) \left( \frac{9}{8} \right) = 15300 \]

### Step 6: Solve for \( x \)
First, multiply both sides by \( \frac{8}{9} \):
\[ \frac{19x}{15} - 2550 = 15300 \cdot \frac{8}{9} \]
Calculating the right side:
\[ 15300 \cdot \frac{8}{9} = 13600 \]
So we have:
\[ \frac{19x}{15} - 2550 = 13600 \]
Now, add 2550 to both sides:
\[ \frac{19x}{15} = 13600 + 2550 = 16150 \]
Next, multiply both sides by \( 15 \):
\[ 19x = 16150 \cdot 15 \]
Calculating the right side:
\[ 16150 \cdot 15 = 242250 \]
Now, divide both sides by 19:
\[ x = \frac{242250}{19} = 12750 \]

### Conclusion
Ramu's initial income is Rs. 12,750.

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