Question

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

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

Hint:

Let incomes be 7x and 3x, subtract Rs. 300 from each to get expenses, then use the expense ratio.

Answer 1

The Correct Option is C

Step 1: Represent the incomes using the given ratio.
Let the weekly incomes of the two persons be \(7x\) and \(3x\), since their ratio is \(7:3\).

Step 2: Write the expenses in terms of savings.
Since savings = income - expense, and each person saves Rs. 300, expense of the first person \(= 7x - 300\) and expense of the second person \(= 3x - 300\).

Step 3: Use the given expense ratio to form an equation.
The expenses are in ratio \(5:2\), so \(\frac{7x-300}{3x-300} = \frac{5}{2}\). Cross-multiplying, \(2(7x-300) = 5(3x-300)\), which gives \(14x - 600 = 15x - 1500\).

Step 4: Solve for \(x\) and check the wrong options.
Rearranging, \(1500 - 600 = 15x - 14x\), so \(x = 900\). Option A, Rs. 7500, option B, Rs. 4500, and option D, Rs. 5400, do not come from this equation and fail when checked against the expense ratio.

Final Answer:
Weekly income of the first person \(= 7x = 7 \times 900\) \[ \boxed{= \text{Rs. } 6300} \]