Question

The population of a certain town was 50,000. In a year, male population was increased by 5% and female population was increased by 3%. Now the population became 52020. Then what was the number of males and females in the previous year?

Answer 1

Step 1: Read the given word problem carefully and try to understand it.

Step 2: Make assumptions using two variables x and y. 

Let the number of males in previous year be ‘x’ and the number of females be ‘y’.

Step 3: From the given information, form mathematical statements using the above variables. According to the first condition,

the total population of town was 50,000.

 ∴ x + y = 50000 …(i)

 Male population increased by 5%.

 ∴ Number of males = x + 5% of x , 5

Female population increased by 3%. 

∴ Number of females = y + 3% of y

According to the second condition, 

in a year population became 52020 

∴ \(\frac{105}{100}x\) + \(\frac{103}{100}y\) = 5202000

∴ 105 x + 103 y = 5202000 …(ii) 

Multiplying equation (i) by 103, 

103 x + 103 y = 5150000 …(iii) 

Step 4: Here, we use elimination method.

 Subtracting equation (iii) from (ii),

∴ x = 26000 

Substituting x = 26000 in equation (i), 

∴ 26000 + y = 50000 

∴ y = 50000 – 26000 

∴ y = 24000 

∴ Number of males = x = 26000 

∴ Number of females = y = 24000

Step 5:  The number of males and females in the previous year were 26,000 and 24,000 respectively.