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Select the correct answerThe population of a village was 9800. In a year, with the increase in population of males by 8% and that of females by 5%, the population of the village became 10,458.What was the number of males in the village before increase?Options5,6004,2004,4106,048

Question

Select the correct answerThe population of a village was 9800. In a year, with the increase in population of males by 8% and that of females by 5%, the population of the village became 10,458.What was the number of males in the village before increase?Options5,6004,2004,4106,048

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Solution

Let's denote the number of males in the village before the increase as M, and the number of females as F. We know from the problem that:

M + F = 9800 (since this was the total population of the village before the increase)

We also know that after the increase, the population of the village became 10,458. The increase in population of males was 8% and that of females was 5%. So we can write:

1.08M + 1.05F = 10,458

Now we have a system of two equations, and we can solve it step by step.

First, let's express F from the first equation:

F = 9800 - M

Now we can substitute F in the second equation:

1.08M + 1.05(9800 - M) = 10,458

Let's simplify this:

1.08M + 10290 - 1.05M = 10,458

Combine like terms:

0.03M = 168

Finally, solve for M:

M = 168 / 0.03 = 5600

So, the number of males in the village before the increase was 5600.

This problem has been solved

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