Question

The salary of Manu is half of that of Tanu. If Manu's salary increases by Rs. 3,000 and Tanu's salary decreases by 20%, then Manu's salary would be 68.75% of Tanu's salary. What is the salary of Tanu?

• A. Rs 1,20,000
• B. Rs 45,000
• C. Rs 90,000
• D. Rs.60,000

Answer 1

The Correct Option is D

Salary Calculation for Tanu and Manu 

Step 1: Define the Variables

Let the salary of Tanu be T and the salary of Manu be M.

According to the given condition, we have:

\[ M = \frac{T}{2} \]

Step 2: Analyze the Changes in Salaries

After the changes:

• Manu's salary increases by Rs. 3,000, so his new salary is \( M + 3000 \).
• Tanu's salary decreases by 20%, so her new salary is \( 0.8T \).

We are also given that Manu’s new salary is 68.75% of Tanu’s new salary. Therefore, we can write the equation:

\[ M + 3000 = 0.6875 \times 0.8T \]

Step 3: Substitute and Simplify the Equation

Substitute \( M = \frac{T}{2} \) into this equation:

\[ \frac{T}{2} + 3000 = 0.6875 \times 0.8T \]

Simplify the right side:

\[ \frac{T}{2} + 3000 = 0.55T \]

Step 4: Solve for T

Multiply the entire equation by 2 to eliminate the fraction:

\[ T + 6000 = 1.1T \]

Rearrange the terms:

\[ 6000 = 1.1T - T \] \[ 6000 = 0.1T \] \[ T = \frac{6000}{0.1} = 60,000 \]

Final Answer:

The salary of Tanu is Rs. 60,000.

Conclusion:

The correct answer is (d) Rs. 60,000.