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?
50%
To solve this problem, we need to find the monthly salary of M first and then express it as a percentage of P's monthly salary. This requires using the given average salary information step by step.
Monthly Salary Data Breakdown
Let's list the information provided in the question clearly:
- The average monthly salary of M, N, and S is ₹ 4000.
- The average monthly salary of N, S, and P is ₹ 5000.
- The monthly salary of P is ₹ 6000.
Our goal is to find M's monthly salary and then calculate what percentage it is of P's monthly salary.
Calculating Total Monthly Salaries from Averages
The formula for average is: Average = (Sum of values) / (Number of values). This means we can find the sum of salaries by multiplying the average salary by the number of people.
Total Monthly Salary of M, N, and S
Given the average monthly salary of M, N, and S is ₹ 4000, and there are 3 individuals:
Total monthly salary of M, N, S = Average monthly salary \(\times\) Number of individuals
Total monthly salary of M, N, S = \(₹ 4000 \times 3\)
Total monthly salary of M, N, S = \(₹ 12000\)
We can write this as an equation:
\[ \text{M} + \text{N} + \text{S} = 12000 \quad \cdots (1) \]
Total Monthly Salary of N, S, and P
Given the average monthly salary of N, S, and P is ₹ 5000, and there are 3 individuals:
Total monthly salary of N, S, P = Average monthly salary \(\times\) Number of individuals
Total monthly salary of N, S, P = \(₹ 5000 \times 3\)
Total monthly salary of N, S, P = \(₹ 15000\)
We can write this as an equation:
\[ \text{N} + \text{S} + \text{P} = 15000 \quad \cdots (2) \]
Determining Individual Monthly Salaries
Now we will use the given monthly salary of P to find the other unknown salaries.
Combined Monthly Salary of N and S
We know that the monthly salary of P is ₹ 6000. We can substitute this value into equation (2):
From equation (2):
\[ \text{N} + \text{S} + \text{P} = 15000 \]
Substitute \(\text{P} = 6000\):
\[ \text{N} + \text{S} + 6000 = 15000 \]
To find the combined monthly salary of N and S, subtract 6000 from both sides:
\[ \text{N} + \text{S} = 15000 - 6000 \]
\[ \text{N} + \text{S} = 9000 \quad \cdots (3) \]
So, the combined monthly salary of N and S is ₹ 9000.
Monthly Salary of M
Now that we know the combined monthly salary of N and S, we can substitute this value into equation (1) to find M's monthly salary.
From equation (1):
\[ \text{M} + \text{N} + \text{S} = 12000 \]
Substitute \(\text{N} + \text{S} = 9000\) from equation (3):
\[ \text{M} + 9000 = 12000 \]
To find M's monthly salary, subtract 9000 from both sides:
\[ \text{M} = 12000 - 9000 \]
\[ \text{M} = 3000 \]
Thus, the monthly salary of M is ₹ 3000.
Monthly Salary Percentage Calculation
Finally, we need to express M's monthly salary as a percentage of P's monthly salary.
- Monthly salary of M = ₹ 3000
- Monthly salary of P = ₹ 6000 (given in the question)
The formula for calculating a percentage is:
\[ \text{Percentage} = \left( \frac{\text{Value of M}}{\text{Value of P}} \right) \times 100\% \]
Substitute the respective monthly salaries:
Percentage = \(\left( \frac{3000}{6000} \right) \times 100\%\)
Percentage = \(\left( \frac{1}{2} \right) \times 100\%\)
Percentage = \(0.5 \times 100\%\)
Percentage = \(50\%\)
Therefore, the monthly salary of M is 50% of the monthly salary of P.
| Individual | Monthly Salary (₹) |
|---|---|
| M | 3000 |
| P | 6000 |
| N + S | 9000 |
The calculation shows that M's salary is exactly half of P's salary, which translates to 50%.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
