Multiple choice

The ratio of the incomes of A and B is 3 : 5, whereas the ratio of their expenditures is 4 : 7, respectively. If A and B save Rs. 16,000 and Rs. 26,000, respectively, then what is the difference (in Rs.) between their expenditures?

  1. 6,800

  2. 5,400

  3. 5,000

  4. 6,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Income A=3x, B=5x. Expenditure A=4y, B=7y. 3x-4y=16000, 5x-7y=26000. Multiply first by 5, second by 3: 15x-20y=80000, 15x-21y=78000. Subtract: y=2000. Expenditures are 4y=8000 and 7y=14000. Difference = 6000.

AI explanation

Let A's income and expenditure be 3x and 4y, and B's be 5x and 7y. Using the savings formula, Income minus Expenditure equals Savings, we get 3x - 4y = 16000 and 5x - 7y = 26000. Multiplying the first equation by 5 gives 15x - 20y = 80000, and multiplying the second by 3 gives 15x - 21y = 78000; subtracting them yields y = 2000. The difference between their expenditures is 7y - 4y, which equals 3y, so 3 multiplied by 2000 is 6000. The difference is Rs. 6000.

Keep practicing — related questions