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.?

Option 5 : 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