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The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

Question

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

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Solution

Sure, let's solve this step by step:

Step 1: Let's assume the number of boys in the college is 7x and the number of girls is 8x.

Step 2: According to the problem, the number of boys increased by 20% and the number of girls increased by 10%.

Step 3: So, the new number of boys is 7x + 20/100 * 7x = 7x * (1 + 20/100) = 7x * 1.2 = 8.4x.

Step 4: Similarly, the new number of girls is 8x + 10/100 * 8x = 8x * (1 + 10/100) = 8x * 1.1 = 8.8x.

Step 5: Therefore, the new ratio of boys to girls is 8.4x : 8.8x.

Step 6: This ratio can be simplified by dividing both sides by 0.4x, which gives us 21 : 22.

So, the new ratio of boys to girls in the college is 21 : 22.

This problem has been solved

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