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

Since this is a multiple-choice question, we can check each option directly against both ratio conditions instead of solving equations from scratch.

Try option C: first person's weekly income is Rs. 6300. Since income ratio is $7:3$, one unit of ratio is $6300/7 = 900$, so the second person's income is $3 \times 900 = 2700$.

Each person saves Rs. 300, so expenses are: first person, $6300 - 300 = 6000$; second person, $2700 - 300 = 2400$.

Check the expense ratio: $6000 : 2400$ simplifies by dividing both by 1200, giving $5 : 2$, exactly matching the condition given in the question.

Let's summarize:

• Income ratio: $6300 : 2700 = 7 : 3$, correct
• Expense ratio after saving Rs. 300 each: $6000 : 2400 = 5 : 2$, correct

Both conditions hold exactly, so option C, Rs. 6300, must be the weekly income of the first person.