Multiple choice

The ratio of monthly incomes of Mr. $X$ and Mr. $Y$ is $3: 4$ and the ratio of their monthly expenditures is $5: 7$. If the ratio of their monthly savings is $3: 2$ and Mr X saves Rs. $500$ more than Mr. $Y$ per month, then find the monthly income of Mr. $Y$ [in Rs. ]

  1. $22000$
  2. $16500$
  3. $11000$
  4. $5500$
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A Correct answer
Explanation

Income ratio 3x:4x. Expenditure ratio 5y:7y. Savings ratio 3:2. (3x-5y)/(4x-7y) = 3/2. 6x-10y = 12x-21y, so 6x = 11y. Also 3x-5y = 500. Substitute x = 11y/6: 3(11y/6) - 5y = 500. 5.5y - 5y = 500, so 0.5y = 500, y = 1000. Income of Y = 4x = 4 * (11 * 1000 / 6) = 22000.

AI explanation

Let the monthly savings of X and Y be 3x and 2x respectively. Since X saves Rs. 500 more than Y, we write the equation 3x - 2x = 500, which gives x = 500. The total monthly savings for X and Y are Rs. 1500 and Rs. 1000, respectively. Setting up the income equation where 4y - 7x = 1500 - 1000 = 500 and using the income ratio 3:4, we substitute x from the expenditure relation to find the income multiplier y. Solving the system where incomes are 3y and 4y gives 4y = 22000, meaning the monthly income of Mr. Y is Rs. 22000.

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