Question

1. The present population of a town is 31,250. If the annual increase in population is 4%, what will be the population of the town after 3 years?​

Answer 1

Answer:

35,000

Step-by-step explanation:

Present Population : 31,250

Annual increase in population : 4% per year

Population after 3 years = ?

Total increase % in 3 years = 4% × 3 = 12%

Population after 3 years = 31250 × $\frac{12}{100}$

                                        = 3750

31250 + 3750 = 35000

Therefore,The population of the town after 3 years will be 35,000.

Answer 2

Answer:

Question No 1 :-

• The present population of a town is 31250. If the annual increase in population is 4%, what will be the population of the town after 3 years.

Given :-

• The present population of a town is 31250.
• The annual increase in population is 4%.

To Find :-

• What is the population of the town after 3 years.

Formula Used :-

$\clubsuit$ Amount Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{A =\: P\bigg(1 + \dfrac{r}{100}\bigg)^n}}}\: \: \: \bigstar$

where,

• A = Amount
• P = Present Population
• r = Rate of Growth
• n = Time Period

Solution :-

Let,

$\mapsto$ The population of the town after 3 years be A.

Given :

• Present Population = 31250
• Rate of Growth = 4%
• Time Period = 3 years

According to the question by using the formula we get,

$\implies \sf A =\: 31250\bigg(1 + \dfrac{4}{100}\bigg)^3$

$\implies \sf A =\: 31250\bigg(\dfrac{104}{100}\bigg)^3$

$\implies \sf A =\: 31250\bigg(\dfrac{104}{100} \times \dfrac{104}{100} \times \dfrac{104}{100}\bigg)$

$\implies \sf A =\: 31250\bigg(\dfrac{1124864}{1000000}\bigg)$

$\implies \sf A =\: \dfrac{35152\cancel{000000}}{1\cancel{000000}}$

$\implies \sf A =\: \dfrac{35152}{1}$

$\implies \sf\bold{\red{A =\: 35152}}$

$\therefore$ The population of the town after 3 years is 35152 .

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Question No 2 :-

• The value of a scooter is decreasing at the rate of 15% per year. Find its value after 2 years if its value was ₹ 70000 at the time of purchase.

Given :-

• The value of a scooter is decreasing at the rate of 15% per year.

To Find :-

• What is the value after 2 years if its value was ₹ 70000 at the time of purchase.

Formula Used :-

$\clubsuit$ Amount Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{A =\: P\bigg(1 - \dfrac{r}{100}\bigg)^n}}}\: \: \: \bigstar$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time Period

Solution :-

$\mapsto$ The value of scooter after 2 years be A.

Given :

• Principal = ₹ 70000
• Rate of Interest = 15% per year
• Time Period = 2 years

According to the question by using the formula we get,

$\implies \sf A =\: 70000\bigg(1 - \dfrac{15}{100}\bigg)^2$

$\implies \sf A =\: 70000\bigg(\dfrac{85}{100}\bigg)^2$

$\implies \sf A =\: 70000\bigg(\dfrac{85}{100} \times \dfrac{85}{100}\bigg)$

$\implies \sf A =\: 70000\bigg(\dfrac{7225}{10000}\bigg)$

$\implies \sf A =\: \dfrac{50575\cancel{0000}}{1\cancel{0000}}$

$\implies \sf A =\: \dfrac{50575}{1}$

$\implies \sf\bold{\red{A =\: ₹\: 50575}}$

$\therefore$ The value of a scooter after 2 years is ₹ 50575 .

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