The population of a town is 20,000. If the Males increase by 3% and the females by 4% the population will be 20680. How many females are there?a)8000b)12000c)9000d)10000Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Solution:

Let's assume the number of males in the town is M and the number of females is F.

According to the given information, the population of the town is 20,000, so we can write the equation:

M + F = 20,000 ------------------(1)

We are also given that if the number of males increases by 3% and the number of females increases by 4%, the population will be 20,680. Mathematically, we can write this as:

M + 0.03M + F + 0.04F = 20,680

Simplifying this equation, we get:

1.03M + 1.04F = 20,680 ----------------(2)

Now, we have two equations with two unknowns (M and F). We can solve these equations simultaneously to find the values of M and F.

To solve the equations, we can use the elimination method. Multiplying equation (1) by 1.03, we get:

1.03M + 1.03F = 20,600 ----------------(3)

Now, subtracting equation (3) from equation (2), we get:

(1.03M + 1.04F) - (1.03M + 1.03F) = 20,680 - 20,600

0.01F = 80

Dividing both sides of the equation by 0.01, we get:

F = 80 / 0.01

F = 8000

Therefore, the number of females in the town is 8000. Hence, the correct answer is option A.

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