Question: The value of a car depreciates at the rate of 10% per annum. If its present value is Rs. 121500, then what was the value of the car two years ago?

(A) Rs. 100000
(B) Rs. 150000
(C) Rs. 200000
(D) Rs. 250000
(E) Rs. 300000

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:

• The value of a car depreciates at the rate of 10% per annum.
• Its present value is Rs. 121500

Find out:

• The value of the car two years ago.

As per the formula of Depreciation, we know that:
=> A = \(P ( 1- \frac{R}{100})^T\) where A = present value, R = rate, P = previous value and T = time.
As per the conditions of the problem, we know that:
A= 121500
R= 10
T=2
It is required to find the value of P.
Therefore, by plugging the values in the formula of depreciation [ A = \(P ( 1- \frac{R}{100})^T\) ], we get:
=> 121,500 = \(P ( 1- \frac{10}{100})^2\)
=> 121,500 = \(P *\frac{9}{10}*\frac{9}{10}\)
=> P = \(\frac{121500 * 10 *10}{9*9}\)
=> P = 150,000
Hence, the value of the car two years ago = 150,000.

Approach Solution 2:
The problem statement implies that:
Given:

• The value of a car depreciates at the rate of 10% per annum.
• Its present value is Rs. 121500

Find out:

• The value of the car two years ago.

If it depreciates by 10% each year, this implies that the value of the car is multiplied by 0.9 each year.
Hence after two years, the original value of the car is multiplied by 0.9^2 = 0.81.
The answers are very far apart, so we can liberally estimate.
We want an answer choice that will give us roughly 120,000 when we take roughly 80% of it. From the above answer choices it can be analysed that only 150,000 is at all plausible.
Hence, the value of the car two years ago = 150,000.

Approach Solution 3:
The problem statement suggests that:
Given:

• The value of a car depreciates at the rate of 10% per annum.
• Its present value is Rs. 121500

Find out:

• The value of the car two years ago.

Let’s solve the problem by using the formula i.e: a + b – ab/100
Equivalent rate of depreciation for two years = 10 + 10 - (10 x 10)/100 = 20 - 1 = 19%
Let the value of the car before two years is 100.
The present value = 100 - 19 = 81
81 units = 121500
1 unit = 121500/81
Therefore, 100 units = 121500/81 x 100 = 150,000
Hence, the value of the car two years ago = 150,000.

“The value of a car depreciates at the rate of 10% per annum”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have a basic knowledge of arithmetic, geometry and algebra. The candidates can follow the GMAT Quant practice papers to practise varieties of questions that will help them to improve their mathematical skills.

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