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Explore the intricate balance of incomes: P and Q earn an average of Rs 5050 monthly, while Q and R’s average is Rs 6250, and P and R’s is Rs 5200.
The average monthly income of P and Q is Rs 5050. The average monthly income of Q and R is Rs 6250 and the average monthly income of P and R is Rs 5200. The monthly income of P is
The monthly income of P is Rs 4000.
Let’s denote the monthly incomes of individuals P, Q, and R as P, Q, and R respectively.
We are given:
1. The average monthly income of P and Q is Rs 5050.This can be expressed as: (P + Q) / 2 = 5050
2. The average monthly income of Q and R is Rs 6250.This can be expressed as: (Q + R) / 2 = 6250
3. The average monthly income of P and R is Rs 5200.This can be expressed as: (P + R) / 2 = 5200
Now, we can solve these equations to find the values of P, Q, and R.
From the first equation: (P + Q) / 2 = 5050=> P + Q = 2 * 5050=> P + Q = 10100 (Equation 1)
From the second equation: (Q + R) / 2 = 6250=>Q + R = 2 * 6250=> Q + R = 12500 (Equation 2)
From the third equation: (P + R) / 2 = 5200=> P + R = 2 * 5200=> P + R = 10400 (Equation 3)
Now, we can use these equations to find the value of P.
Add equations 1 and 3:(P + Q) + (P + R) = 10100 + 10400=> 2P + (Q + R) = 20500 (Equation 4)
Substitute the value of (Q + R) from Equation 2 into Equation 4:
2P + 12500 = 20500
=> 2P = 20500 – 12500
=> 2P = 8000
=> P = 8000 / 2
=> P = 4000
So, the monthly income of P is Rs 4000.
What is an Average in Mathematics?
In mathematics, an average is a measure that represents a typical value or central tendency of a set of numbers. There are several types of averages commonly used:
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Arithmetic Mean: This is the most commonly used average. It is calculated by adding up all the values in a set and then dividing by the number of values. For example, the arithmetic mean of the numbers 3, 5, 7, and 9 is (3 + 5 + 7 + 9) / 4 = 6.
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Median: The median is the middle value in a sorted list of numbers. If there is an even number of values, the median is the average of the two middle values. For example, the median of the numbers 3, 5, 7, and 9 is 6, and the median of the numbers 2, 4, 6, 8 is (4 + 6) / 2 = 5.
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Mode: The mode is the value that appears most frequently in a set of numbers. A set of numbers can have one mode, more than one mode, or no mode at all. For example, the mode of the numbers 3, 3, 5, 7, and 9 is 3.
These are the most common types of averages used in mathematics, each providing different insights into the central tendency of a dataset.
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Categories: Math
