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X sold a car to Y at cost price + 30% of cost price. Y further sold the same car to Z for Rs. 550000 earning a profit of 10% on cost price. Z used car for two years charging the depreciation at the rate of 10% per annum with original cost method. After two years he sold the car at a price which is less than 5% of the original value of the car (Cost price of car at which it is purchased by X). Calculate the profit earned or loss suffered by Z.

X sold a car to Y at cost price + 30% of cost price. Y further sold the same car to Z for Rs. 550000 earning a profit of 10% on cost price. Z used car for two years charging the depreciation at the rate of 10% per annum with original cost method. After two years he sold the car at a price which is less than 5% of the original value of the car (Cost price of car at which it is purchased by X). Calculate the profit earned or loss suffered by Z. Correct Answer Rs. 74615.75 loss

Firstly, we need to calculate the original value of the car to find the profit earned or loss suffered by Z

Let the cost at which Y purchased the car be a

⇒ Profit earned by him = 10a/100 = a/10

⇒ Selling price = a + (a/10) = 11a/10

ATQ,

⇒ 11a/10 = 550000

⇒ a = 500000

So, Cost price at which car is purchased by Y = Rs. 500000

Cost price of Y is the selling price of X

Let the original cost at which X has purchased the car be b

⇒ Profit earned by him = 30a/100 = 3a/10

⇒ Selling price = b + (3b/10) = 13b/10

⇒ 500000 = 13b/100

⇒ b = 384615

⇒ The original cost at which X has purchased the car = Rs. 384615

Now, we have to calculate the value of car with Z at the time of selling

⇒ Price at which Z purchased the car = Rs. 550000

⇒ Depreciation for two years at the rate of 10% p.a. = 2 × (10% of 550000) = 2 × 55000 = Rs. 110000

⇒ Value of the car after two years = 550000 – 110000 = Rs. 440000       ---- (1)

⇒ Price at which car is sold by Z = 384615 – (5% of 384615) = 384615 – 19230.75 = Rs. 365384.25        ---- (2)

From equation (1) and (2)

⇒ Loss suffered by Z on sale = 440000 – 365384.25 = 74615.75

∴ The selling price is less than the value of car. So, loss suffered by Z on sale is Rs. 74615.75

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