Total cost price (C.P.) of two cars A and B of different models is ₹5.0 lakhs. Car A is sold at a profit of 20% and car B is sold at a loss of 20%. However, the selling price of the two cars A and B remains the same.

Find the cost price (C.P.) of the two cars A and B in lakhs, respectively

Question

Question

This question was previously asked in

UGC NET Official Paper-I (Held On: 05 Mar, 2023 Shift 2)

Answer 1

Calculation:

Let's denote the cost price of car A as 'a' and the cost price of car B as 'b'.

From the problem, we know two things:

1) The total cost price of two cars A and B is ₹5.0 lakhs. This means a + b = 5.0 (in lakhs).

2) Car A is sold at a profit of 20% and car B is sold at a loss of 20%, but the selling prices of both cars are the same. This means 1.2a = 0.8b.

From the second equation, we can derive a = (0.8/1.2)b = (2/3)b.

Now, substitute this into the first equation:

(2/3)b + b = 5.0

⇒ (5/3)b = 5.0

⇒ b = 3.0 (in lakhs).

Substitute b = 3.0 into the first equation:

a + 3.0 = 5.0

a = 2.0 (in lakhs).

∴ The cost price of car A is ₹2.0 lakh and the cost price of car B is ₹3.0 lakh.