Question

The population of a village when increased by 20%, becomes 25,800. What was the original population​

Answer 1

Answer :-

• The original population of the city was 21500.

Given :-

• The population of a village when increased by 20% becomes 25,800.

To find :-

• The original population of the village.

Step-by-step explanation :-

Let the original population of the village be x.

According to the question, the population when increased by 20% becomes 25,800.

Since the original population is x, therefore we get :-

$\sf \bf x = 25800 - 20\% \:of\:x$

$\sf \bf x = 25800 - \dfrac{20}{100} \:of \:x$

$\sf \bf x = 25800 - \dfrac{1}{5} \:of\:x$

$\sf \bf x = 25800 - \dfrac{x}{5}$

$\sf \bf x + \dfrac{x}{5} = 25800$

$\sf \bf \dfrac{6x}{5} = 25800$

$\sf \bf 6x = 25800 \: \times \: 5$

$\sf \bf 6x = 129000$

$\sf \bf x = \dfrac{129000}{6}$

$\sf \bf x = 21500.$

Thus, the original population of the city was 21500.

$\sf \bf Verification :-$

To check your answer, just add 20% of 21500 to the original population (21500) and see whether you get 25800 or not.

We are taking 20% of 21500 and not 25800 because 20% of 21500 was increased to get 25800.

Now lets proceed!

$\sf \bf 21500 + 20\% \:of\: 21500$

$\sf \bf 21500 \:+ \dfrac{20}{100} \times 21500$

$\sf \bf 21500\: + \: 20\times 215$

$\sf \bf 21500 + 4300$

$\sf \bf = 25800.$

Since we got 25800 after adding 20% of 21500 to the original population,

Hence verified!

Answer 2

Answer :-

The original population of the city was 21500.

Given :-

The population of a village when increased by 20% becomes 25,800.

To find :-

The original population of the village.

Step-by-step explanation :-

Let the original population of the village be x.

According to the question, the population when increased by 20% becomes 25,800.

Since the original population is x, therefore we get :-

\sf \bf x = 25800 - 20\% \:of\:xx=25800−20%ofx

\sf \bf x = 25800 - \dfrac{20}{100} \:of \:xx=25800−

100

20

ofx

\sf \bf x = 25800 - \dfrac{1}{5} \:of\:xx=25800−

5

1

ofx

\sf \bf x = 25800 - \dfrac{x}{5}x=25800−

5

x

\sf \bf x + \dfrac{x}{5} = 25800x+

5

x

=25800

\sf \bf \dfrac{6x}{5} = 25800

5

6x

=25800

\sf \bf 6x = 25800 \: \times \: 56x=25800×5

\sf \bf 6x = 1290006x=129000

\sf \bf x = \dfrac{129000}{6}x=

6

129000

\sf \bf x = 21500.x=21500.

Thus, the original population of the city was 21500.

:-Verification:−

To check your answer, just add 20% of 21500 to the original population (21500) and see whether you get 25800 or not.

We are taking 20% of 21500 and not 25800 because 20% of 21500 was increased to get 25800.

Now lets proceed!

\sf \bf 21500 + 20\% \:of\: 2150021500+20%of21500

\sf \bf 21500 \:+ \dfrac{20}{100} \times 2150021500+

100

20

×21500

\sf \bf 21500\: + \: 20\times 21521500+20×215

\sf \bf 21500 + 430021500+4300

\sf \bf = 25800.=25800.

Since we got 25800 after adding 20% of 21500 to the original population,