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Question: The average monthly income of four members of a family is \(610.25\) Rs after the marriage of one gi...

The average monthly income of four members of a family is 610.25610.25 Rs after the marriage of one girl the average income of the family becomes 650.75650.75 Rs, then what is the salary of a married girl?
A) 488.25488.25 Rs
B) 488.75488.75 Rs
C) 479.75479.75 Rs
D) 489.25489.25 Rs

Explanation

Solution

In this question, we are given the average monthly income of four members of a family and also the average income when one of the members leaves. Using both, we will find the sum of the income of four members and three members combined. Subtract both of them and you will get the monthly income of the person who left as the difference in sum is due to the person leaving.

Complete step-by-step solution:
We are given the average monthly income of four members. Let us find the sum of their income first using the formula, Mean = Sum of observationsTotal observations\dfrac{{{\text{Sum of observations}}}}{{{\text{Total observations}}}}.
It is given that, mean = 610.25610.25 Rs and total members = 44.
Putting the values in the formula,
⇒610.25=Sum4\Rightarrow 610.25 = \dfrac{{{\text{Sum}}}}{4}
Solving,
⇒Sum = 610.25×4=2441\Rightarrow {\text{Sum = }}610.25 \times 4 = 2441Rs
Therefore, the combined salary of the four members of family is Rs.24412441
Now, we know that the mean of the three members of the family is 650.75650.75 Rs.
Putting the values in the formula to find the sum of their salaries.
⇒650.75=Sum3\Rightarrow 650.75 = \dfrac{{{\text{Sum}}}}{3}
Solving,
⇒Sum = 650.75×3 = 1952.25\Rightarrow {\text{Sum = 650}}{\text{.75}} \times {\text{3 = 1952}}{\text{.25}}Rs
Therefore, the combined salary of the three members of family is Rs.1952.251952.25
Now the difference in the combined salary of four and three members will give us the salary of the girl who got married.
⇒2441−1952.25=488.75\Rightarrow 2441 - 1952.25 = 488.75

Therefore, the salary of the married girl is Rs.488.75488.75.

Note: If the students are finding difficulty in understanding the reason behind that why we subtracted the two sums can understand it by the following equation-
⇒\Rightarrow Combined salary of three members + salary of married girl = combined salary of four members
⇒\Rightarrow Salary of married girl = combined salary of four members - combined salary of three members