Question

Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves Rs. 300 per week, then the weekly income of the first person is

• A. Rs. 7500
• B. Rs. 4500
• C. Rs. 6300
• D. Rs. 5400

Answer 1

The Correct Option is C

To solve the problem, we will set up equations based on the information provided:
Let the weekly incomes of the two persons be \( 7x \) and \( 3x \) respectively, and their weekly expenses be \( 5y \) and \( 2y \). Given that each of them saves Rs. 300 per week, we can write the following equations:
1. For the first person: \( 7x - 5y = 300 \)
2. For the second person: \( 3x - 2y = 300 \)

We have a system of linear equations:
\( 7x - 5y = 300 \) (Equation 1)
\( 3x - 2y = 300 \) (Equation 2)

We will solve these simultaneous equations. First, we multiply Equation 2 by 5 and Equation 1 by 2 to align the coefficients of \( y \):
\( 15x - 10y = 1500 \) (from Equation 2)
\( 14x - 10y = 600 \) (from Equation 1)

Subtract the second modified equation from the first:
\( (15x - 10y) - (14x - 10y) = 1500 - 600 \)
\( x = 900 \)

Now that we know \( x \), substitute \( x = 900 \) into Equation 1:
\( 7(900) - 5y = 300 \)
\( 6300 - 5y = 300 \)
\( 5y = 6000 \)
\( y = 1200 \)

Now calculate the weekly income of the first person:
\( 7x = 7(900) = 6300 \)

Thus, the weekly income of the first person is Rs. 6300.