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प्रश्न
The ratio of the annual income of A and B is 6 : 5 and the ratio of their expenditures is 5 : 4. If each saves ₹ 10000, find their annual incomes.
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उत्तर
Given:
- Ratio of annual incomes of A and B = 6 : 5
- Ratio of their expenditures = 5 : 4
- Each saves ₹ 10,000
Step-wise calculation:
1. Let the annual income of A = 6x and the annual income of B = 5x.
2. Let the annual expenditure of A = 5y and the annual expenditure of B = 4y.
3. Since savings = income – expenditure, we have:
For A: 6x – 5y = 10,000
For B: 5x – 4y = 10,000
4. Multiply the first equation by 4 and the second by 5 to make the y terms comparable:
(6x – 5y) × 4 → 24x – 20y = 40,000
(5x – 4y) × 5 → 25x – 20y = 50,000
5. Subtract the first new equation from the second:
(25x – 20y) – (24x – 20y) = 50,000 – 40,000
x = 10,000
6. Put x = 10,000 into one of the earlier equations:
6(10,000) – 5y = 10,000
60,000 – 5y = 10,000
5y = 60,000 – 10,000
5y = 50,000
y = 10,000
7. Calculate annual incomes:
Income of A = 6x
Income of A = 6 × 10,000
Income of A = ₹ 60,000
Income of B = 5x
Income of B = 5 × 10,000
Income of B = ₹ 50,000
The annual income of A is ₹ 60,000 and the annual income of B is ₹ 50,000.
