Multiple choice

In a class the ratio of the number of boys to that of the girls is $7: 3$. Each boy is given only a $50$ paise coin and each girl is given a $75$ paise coin (assuming $75$ paise coins are available) The difference in the amount present with the boys and the girls is Rs. $3.75$. How many coins should the boys and girls exchange so that the amount with the boys becomes twice the amount with the girls?

  1. $8$
  2. $6$
  3. $4$
  4. $9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boys be 7x and girls be 3x. Boys have 350x paise, girls have 225x paise. Difference 125x = 375, so x = 3. Boys have 21, girls 9. Total amounts are 1050 and 675. After exchanging coins, the ratio must be 2:1. Solving for the number of coins leads to 4.

AI explanation

Based on the 7:3 ratio, let the number of boys be 7x and the number of girls be 3x. The total amount with the boys is 0.50 * 7x = 3.5x, and the total amount with the girls is 0.75 * 3x = 2.25x. The difference is 3.5x - 2.25x = 1.25x, which equals Rs. 3.75, meaning x = 3. There are 21 boys and 9 girls initially. If y coins are exchanged, the boys' new amount is 10.50 + 0.25y and the girls' new amount is 6.75 - 0.25y. Setting the boys' amount to twice the girls' amount gives 10.50 + 0.25y = 2(6.75 - 0.25y), which solves to 0.75y = 3, so y = 4.

Keep practicing — related questions