Question

Population of a town is 9000. If the males
by 8%. and the females increase
by 5%.the population will be 9600. Then the
number of males of the town initially was​

Answer 1

The number of males initially was 5000.

Given:

• The population of a town is 9000.
• If the males by 8% and the females increase by 5%.
• The population will be 9600.

To find:

• Find the number of males in the town initially.

Solution:

Step 1:

Write the equations.

Let the number of men be 'x' and women be 'y'.

$\bf x + y = 9000...eq1$

And

$108\% \: of \: x + 105\% \: of \: y = 9600$

$\frac{108}{100} x + \frac{105}{100}y = 9600$

$\bf 108x + 105y = 960000...eq2$

Step 2:

Solve the equations.

Multiply eq1 by 105 and subtract both equations.

$108x + 105y = 960000 \\ 105x + 105y = 945000 \\ ( - ) \: \: \: ( - ) \: \: \: \: ( - ) \: \: \: \: \: \: \: \: \\ - - - - - - - - - - - \\ 3x = 15000 \\ - - - - - - - - - - -$

$3x = 15000$

$x = \frac{15000}{3}$

$\bf x = 5000$

Thus,

The number of males initially was 5000.

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Answer 2

The number of males of the town initially was 5000

Given :

• Population of a town is 9000.

• The males by 8% and the females increase by 5% the population will be 9600

To find :

The number of males of the town initially

Solution :

Step 1 of 2 :

Form the equation to calculate number of males of the town initially

Let number of males of the town initially was n

Since total population of the town = 9000

∴ Number of females of the town initially = 9000 - n

Again males by 8% and the females increase by 5% the population will be 9600

By the given condition

$\displaystyle \sf n \times \frac{108}{100} + (9000 - n) \times \frac{105}{100} = 9600$

Step 2 of 2 :

Calculate number of males of the town initially

$\displaystyle \sf n \times \frac{108}{100} + (9000 - n) \times \frac{105}{100} = 9600$

$\displaystyle \sf \implies \frac{108n}{100} + \frac{105(9000 - n)}{100} = 9600$

$\displaystyle \sf{ \implies }108n + 945000 - 105n = 960000$

$\displaystyle \sf{ \implies }3n = 960000 - 945000$

$\displaystyle \sf{ \implies }3n = 15000$

$\displaystyle \sf{ \implies }n = 5000$

Hence number of males of the town initially was 5000

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