Multiple choice

The amounts of pocket money of Rohan and Sumit are in ratio 4 : 7. They spend the money in the ratio 3 : 5, respectively. Rohan saves Rs. 500 from his pocket money and Sumit saves Rs. 1,000. Find the pocket money of Rohan and Sumit.

  1. Rohan = Rs. 1,800, Sumit = Rs. 3,150

  2. Rohan = Rs. 2,000, Sumit = Rs. 3,500

  3. Rohan = Rs. 2,400, Sumit = Rs. 4,200

  4. Rohan = Rs. 2,800, Sumit = Rs. 4,900

  5. Rohan = Rs. 1,600, Sumit = Rs. 2,800
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B Correct answer
Explanation

Let pocket money be 4x and 7x. Spending is 3y and 5y. 4x - 3y = 500 and 7x - 5y = 1000. Multiply first by 5 and second by 3: 20x - 15y = 2500 and 21x - 15y = 3000. Subtracting gives x = 500. Rohan = 4*500 = 2000, Sumit = 7*500 = 3500.

AI explanation

Let the pocket money of Rohan and Sumit be 4x and 7x, and their expenditures be 3y and 5y. We have 4x - 3y = 500 and 7x - 5y = 1000. Multiplying the first equation by 5 and the second by 3 gives 20x - 15y = 2500 and 21x - 15y = 3000, resulting in x = 500. Therefore, Rohan's pocket money is 4(500) = 2000 and Sumit's is 7(500) = 3500.

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