Rohit purchased a car and a plot at the same time. At the end of the first two years the value of the plot increased by 30% and the value of the car decreased by 10%. At the end of next two years, the value of the car decreased by 20% and the value of the plot increased by 25%. At the end of next two years, the value of the plot increased by 20% and the value of car is decreased by 25%. Had he sold both the car and the plot at the end of sixth year, he would have got 56% more from the plot than from the car. How much less did he pay for the plot that the car when he purchased them?

Question

A bought a phone from a store and paid \(\frac{1}{6}\) of the price using UPI, \(\frac{1}{3}\) of the price in cash, and the remaining balance a year later. He also paid 10% interest on the remaining balance after one year. What was the original price of the phone?

Answer 1

The correct answer is option (B):

0.46

Let's analyze this problem step by step to determine the relationship between the initial costs of the car and the plot.

Let's denote the initial price of the car as C and the initial price of the plot as P.

Year 1-2:

* Plot value increases by 30%: P becomes 1.3P
* Car value decreases by 10%: C becomes 0.9C

Year 3-4:

* Plot value is unchanged: 1.3P remains 1.3P
* Car value decreases by 20%: 0.9C becomes 0.9C * 0.8 = 0.72C

Year 5-6:

* Plot value increases by 20%: 1.3P becomes 1.3P * 1.2 = 1.56P
* Car value decreases by 25%: 0.72C becomes 0.72C * 0.75 = 0.54C

At the end of the sixth year:

* Value of the plot: 1.56P
* Value of the car: 0.54C

The problem states that the plot's value is 56% more than the car's value at the end of the sixth year. This translates to the equation:

1. 56P = 0.54C + 0.56 * 0.54C
2. 56P = 0.54C * 1.56
3. 56P = 0.8424C

Now, we need to find the difference between the initial prices, which is C - P (or P - C, we'll deal with the sign later). Let's express P in terms of C:

P = (0.8424 / 1.56) * C
P = 0.54C

Therefore, the difference between the initial prices is C - P = C - 0.54C = 0.46C

Since the question asks "How much less did he pay for the plot than the car...", and we have found that P = 0.54C then, the cost of the plot is less than the cost of the car.

To solve the percentage difference:

Difference = C-P = C - 0.54C = 0.46C

Therefore the plot cost 0.46 less than the car.

The correct answer is 0.46.

The Correct Option is B

Solution and Explanation

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