Question

The price of a machine in a leather factory depreciates at the rate of 10% every year. If the present price of the machine be Rs 100000, let us calculate what will be the price of that machine after 3 years. ​

Answer 1

Solution :

Here , the present price of the machine is Rs. 100, 000 .

The price decreases regularly at a rate of 10% per annum .

We need to find what will be it's price after 3 years .

So , in the present , the price is Rs. 100,000

The next year , it will be decreased by 10%

Or in other terms , it will be 90% of what it was previously ; 90% of the price in the previous year.

So ,

In Year 1 :

New Price -

=> 90% of orginal price

=> 90% of 100,000

=> 90 × 1000

=> 90,000

In the second year the same thing will repeat

New price = 90% of what it was in the first year

=> 90% of 90,000

=> 90 × 900

=> 81, 000

In the third year

Price -

=> 90% of the price in the second year

=> 90% of 81,000

=> 90 × 810

=> 72900

Thus , the required price after 3 years is 72,900.

This is the required answer.

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Answer 2

Answer:

Given :-

• The price of a machine in a leather factory depreciates at the rate of 10% every year and the present price of the machine be Rs 100000.

To Find :-

• What is the price of that machine after 3 years.

Formula Used :-

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

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• t = Time

Solution :-

Given :

• Principal = Rs 100000
• Rate of Interest = 10%
• Time = 3 years

According to the question by using the formula we get,

⇒ $\sf A\: =\: 100000\bigg(1 - \dfrac{10}{100}\bigg)^{3}$

⇒ $\sf A\: =\: 100000\bigg(1 - \dfrac{\cancel{10}}{\cancel{100}}\bigg)^{3}$

⇒ $\sf A\: =\: 100000\bigg(1 - \dfrac{1}{10}\bigg)^{3}$

⇒ $\sf A\: =\: 100000\bigg(\dfrac{9}{10}\bigg)^{3}$

⇒ $\sf A\: =\: 100000 \times \dfrac{9}{10} \times \dfrac{9}{10} \times \dfrac{9}{10}$

⇒ $\sf A\: =\: \dfrac{72900000}{1000}$

⇒ $\sf A\: =\: \dfrac{\cancel{72900000}}{\cancel{1000}}$

➠ $\sf\red{A\: =\: Rs\: 72900}$

$\therefore$ The price of that machine after 3 years is Rs 72900 .