Question

The 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 become 10458. What was the number of males in the village before increase?

• A. $4200$
• B. $4410$
• C. $5600$
• D. $6048$

Answer 1

Answer: (C)

$5600$

Suppose the number of males in the village before increases was $x$.
Then, the number of females $=(9800-x)$
Given, $(x+8\%$ of $x)+(9800-x)+5\%$ of $(9800-x)=10458$
$\Rightarrow 1.08x+1.05\times (9800-x)=10458$
$\Rightarrow 1.08x+1.05\times 9800-1.05x=10458$
$\Rightarrow 0.03x=10458-10290=168$
$\Rightarrow x=\frac{168\times 100}{3}=5600$