# The present cost of a mobile phone is Rs. 15000. If its value decreases every year by 5 %, find the cost of the mobile 2 years ago.

Answer

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Hint: Assign the cost of the mobile before two years to a variable. The value of the mobile decreases by 5 % every year. Hence, find the equation relating the variable to the present cost and find the answer.

Complete step-by-step answer:

We need to determine the cost of the mobile before two years.

Let the cost of the mobile two years ago be x.

The value of the mobile decreases by 5 % every year. Then, before one year the value of the mobile would have decreased by 5 % of x and the actual value one year ago is x – (5 % of x).

Value of mobile one year ago = \[x - \left( {\dfrac{5}{{100}} \times {\text{ }}x} \right)\]

Value of mobile one year ago = \[{\text{ }}x - 0.05{\text{ }}x\]

Value of mobile one year ago = \[{\text{ 0}}{\text{.95 }}x\]

Hence, the value of mobile before one year is 0.95 x.

The present value of mobile would have decreased by 5 % from the previous years, that is, 0.95 x.

The decrease in the value of mobile is 5 % of 0.95 x. The present value of mobile is 0.95 – (5 % of 0.95 x).

Present value of mobile = \[{\text{0}}{\text{.95 }}x - \left( {\dfrac{5}{{100}} \times 0.95x} \right)\]

Present value of mobile = \[{\text{ 0}}{\text{.95 }}x - \left( {0.05 \times 0.95x} \right)\]

Present value of mobile = \[{\text{ 0}}{\text{.95 }}x - 0.0475x\]

Present value of mobile = \[{\text{0}}{\text{.9}}025x\]

It is given that the present value of the mobile is Rs. 15,000. Hence, equating 0.9025x to 15000, we have:

\[0.9025x = 15000\]

Solving for x, we have:

\[x = \dfrac{{15000}}{{0.9025}}\]

\[x = 16620.50\]

Hence, the value of the mobile before two years is Rs. 16620.50

Note: The question asks to find the value of the mobile, two years ago, meaning, two years before. You might make a mistake and calculate the value after two years, which is wrong.

Complete step-by-step answer:

We need to determine the cost of the mobile before two years.

Let the cost of the mobile two years ago be x.

The value of the mobile decreases by 5 % every year. Then, before one year the value of the mobile would have decreased by 5 % of x and the actual value one year ago is x – (5 % of x).

Value of mobile one year ago = \[x - \left( {\dfrac{5}{{100}} \times {\text{ }}x} \right)\]

Value of mobile one year ago = \[{\text{ }}x - 0.05{\text{ }}x\]

Value of mobile one year ago = \[{\text{ 0}}{\text{.95 }}x\]

Hence, the value of mobile before one year is 0.95 x.

The present value of mobile would have decreased by 5 % from the previous years, that is, 0.95 x.

The decrease in the value of mobile is 5 % of 0.95 x. The present value of mobile is 0.95 – (5 % of 0.95 x).

Present value of mobile = \[{\text{0}}{\text{.95 }}x - \left( {\dfrac{5}{{100}} \times 0.95x} \right)\]

Present value of mobile = \[{\text{ 0}}{\text{.95 }}x - \left( {0.05 \times 0.95x} \right)\]

Present value of mobile = \[{\text{ 0}}{\text{.95 }}x - 0.0475x\]

Present value of mobile = \[{\text{0}}{\text{.9}}025x\]

It is given that the present value of the mobile is Rs. 15,000. Hence, equating 0.9025x to 15000, we have:

\[0.9025x = 15000\]

Solving for x, we have:

\[x = \dfrac{{15000}}{{0.9025}}\]

\[x = 16620.50\]

Hence, the value of the mobile before two years is Rs. 16620.50

Note: The question asks to find the value of the mobile, two years ago, meaning, two years before. You might make a mistake and calculate the value after two years, which is wrong.

Last updated date: 30th Sep 2023

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