Multiple choice

The ratio of income of two persons is $9:7$ and the ratio of their expenditure is $4:3$. If each of them saves Rs. $200$ per month, find their monthly income.

  1. Rs. $2200$, Rs. $1400$
  2. Rs. $2100$, Rs. $1400$
  3. Rs. $1800$, Rs. $1400$
  4. Rs. $1900$, Rs. $1400$
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C Correct answer
Explanation

Income ratio 9:7, Expenditure ratio 4:3. Let incomes be 9x, 7x and expenditures be 4y, 3y. Savings: 9x - 4y = 200 and 7x - 3y = 200. Multiply first by 3 and second by 4: 27x - 12y = 600 and 28x - 12y = 800. Subtracting: x = 200. Incomes are 9(200)=1800 and 7(200)=1400.

AI explanation

Let the incomes be 9x and 7x, and the expenditures be 4y and 3y. Their savings are equal, giving the equation 9x minus 4y equals 7x minus 3y, which simplifies to 2x equals y. Since each saves Rs. 200, we also have 9x minus 4y equals 200. Substituting y equals 2x into the savings equation gives x equals 200. The monthly incomes are 9 multiplied by 200, which is Rs. 1800, and 7 multiplied by 200, which is Rs. 1400.

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