Multiple choice

The incomes of two persons are in the ratio of 9 : 7 and their expenditures are in the ratio of 4 : 3. If each of them manages to save Rs. 3,000 per month, find the difference in their income.

  1. 10,000

  2. 5,000

  3. 6,000

  4. 3,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Income ratio 9x:7x, Expenditure ratio 4y:3y. Savings: 9x - 4y = 3000, 7x - 3y = 3000. Multiply first by 3 and second by 4: 27x - 12y = 9000, 28x - 12y = 12000. Subtract: x = 3000. Difference in income = 9x - 7x = 2x = 6000.

AI explanation

Let the incomes of the two persons be 9x and 7x, and their expenditures be 4y and 3y. Their savings give the equations 9x minus 4y equals 3000 and 7x minus 3y equals 3000. Equating the two gives 9x minus 4y equals 7x minus 3y, which simplifies to 2x equals y. Substituting this into the first equation yields 9x minus 8x equals 3000, so x is 3000. The difference in their incomes is 9x minus 7x, which is 2x, resulting in 6000.

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