Question

Q 8) the value of a machine
depreciates 5% every year. If
the present value of the
machine is rupees 100000
what will be its value after 2
years?​

Answer 1

➤ Given :-

Present value of a machine :- ₹100000

Rate of depression :- 5%

Time :- 2 years.

$\:$

➤ To Find :-

The price of machine after two years.

$\:$

★ How to do :-

Here, we are given with the cost of a machine. We are said that the cost of the machine decreases 5% every year. We are asked to find the cost of the same machine after two years. So, first we should find the total rate of depression. Then, we can find the value of the percentage by finding the percent value of present cost. Later, we can subtract the obtained answer with the present cost so that we can find the final answer. So, let's solve!!

$\:$

➤ Solution :-

Decreased price in first year :-

${\tt \leadsto 5 \bf\% \: \: \tt of \: \: 100000}$

Write the percentage as fraction and 'of' as multiplication sign.

${\tt \leadsto \dfrac{5}{100} \times 100000}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{5}{100} \times 100000 = \dfrac{1}{20} \times 100000}$

Now, multiply the remaining numbers.

${\tt \leadsto \dfrac{1 \times 100000}{20} = \dfrac{100000}{20}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{100000}{20} = \dfrac{100000}{20} = 5000}$

Cost of machine in first year :-

${\tt \leadsto 100000 - 5000}$

${\tt \leadsto Rs \: \: 95000}$

$\:$

Now, find the decreased price at second year.

Decreased price in second year :-

${\tt \leadsto 5 \bf\% \: \: \tt of \: \: 95000}$

Write the percentage as fraction and 'of' as multiplication sign.

${\tt \leadsto \dfrac{5}{100} \times 95000}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{5}{100} \times 95000 = \dfrac{1}{20} \times 95000}$

Now, multiply the remaining numbers.

${\tt \leadsto \dfrac{1 \times 95000}{20} = \dfrac{95000}{20}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{95000}{20} = \dfrac{95000}{20} = 4750}$

Cost of machine in second year :-

${\tt \leadsto 95000 - 4750}$

${\tt \leadsto \pink{\underline{\boxed{\tt Rs \: \: 90250}}}}$

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The formula to calculate the percentage is...

${\sf \longrightarrow \underline{\boxed{\sf \dfrac{Part \: of \: value}{Total \: value} \times 100}}}$

Answer 2

❥Given :

• Present value of machine =$100000

• Rate of depreciation = 5%

• Time period = 2 years

❥To find :

• The price of machine after 2 years...

❥Solution :

$• \: \tt \orange{for \: the \: first \: year \: = 5 \: percent\: of \: rs \: 100000}$

$\tt {= rs \: 5000}$

$• \: \tt\orange {value \: of \: the \: machine \: after \: one \: year \: = } \tt\green{rs100000 - rs5000 =}{rs95000 }$

$• \: \tt\orange{value \: of \: the \: machine \: in \: the \: second \: year \: = rs95000}$

$\tt\blue{ = 5 \: percent \: of \: 95000 = } \\ \tt\pink{ \frac{5}{\cancel{{100}}}\green{1} \times{\cancel{ 95000}} \: \: \green{950} \: = }{rs4750}$

$• \: \tt\orange{value \: of \: machine \: after \: 2 \: years \: = } \tt\green{95000 - 4750 \: = }{rs90250}$

$\therefore \: \tt{answer \: = rs90250}$

Important points :-

• write Percentage as "%"

• Make percentage as fraction as I did to solve .

• Of means "×" multiplication.

keep in mind :-

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