Question

The average of the monthly salaries of M, N and S is ₹4000. The average of the monthly salaries of N, S and P is ₹5000. The monthly salary of P is ₹6000.
What is the monthly salary of M as a percentage of the monthly salary of P?

• A. 50%
• B. 75%
• C. 100%
• D. 125%

Hint:

When calculating percentages, always divide the part by the whole and multiply by 100.

Answer 1

The Correct Option is A

Let the monthly salaries of M, N, S, and P be represented by \( m \), \( n \), \( s \), and \( p \), respectively.
1. From the first statement, the average of the monthly salaries of M, N, and S is ₹4000:
\[ \frac{m + n + s}{3} = 4000 \implies m + n + s = 12000. \]
2. From the second statement, the average of the monthly salaries of N, S, and P is ₹5000:
\[ \frac{n + s + p}{3} = 5000 \implies n + s + p = 15000. \]
3. We are given that the monthly salary of P is ₹6000:
\[ p = 6000. \]
Now, subtract the first equation from the second equation:
\[ (n + s + p) - (m + n + s) = 15000 - 12000 \implies p - m = 3000. \]
Substitute \( p = 6000 \):
\[ 6000 - m = 3000 \implies m = 3000. \]
The monthly salary of M is ₹3000. To find the percentage of M's salary with respect to P's salary, we use the formula:
\[ \text{Percentage} = \left( \frac{m}{p} \right) \times 100 = \left( \frac{3000}{6000} \right) \times 100 = 50%. \]
Thus, the correct answer is (A) 50%.