A Samsung duo and a Galaxy are bought for Rs.40000. The Duo is sold at a…

2026

A Samsung duo and a Galaxy are bought for Rs.40000. The Duo is sold at a profit of 33.33% and the Galaxy is sold at a loss of 20%. There was no loss or gain. Find the cost price of the Samsung duo in Rs.

  1. A.

    15000

  2. B.

    25000

  3. C.

    20000

  4. D.

    18000

Attempted by 594 students.

Show answer & explanation

Correct answer: A

Understanding the problem: find the cost price of the Samsung Duo when the two phones together cost Rs.40,000, the Duo is sold at 33 1/3% profit and the Galaxy at 20% loss, and there is no net gain or loss.

Let x = cost price of the Samsung Duo and y = cost price of the Galaxy.

  • Total cost: x + y = 40,000.

  • Selling price of Duo: 33 1/3% = 1/3 profit, so SP_Duo = x + (1/3)x = (4/3)x.

  • Selling price of Galaxy: 20% loss, so SP_Galaxy = y − 0.20y = (4/5)y.

  • No net gain or loss means total selling price = total cost = 40,000, so (4/3)x + (4/5)y = 40,000.

Solve the system:

  1. From x + y = 40,000, substitute y = 40,000 − x into (4/3)x + (4/5)y = 40,000.

  2. (4/3)x + (4/5)(40,000 − x) = 40,000.

  3. Clear denominators by multiplying both sides by 15 (LCM of 3 and 5): 20x + 12(40,000 − x) = 600,000.

  4. Simplify: 20x + 480,000 − 12x = 600,000 ⇒ 8x = 120,000 ⇒ x = 15,000.

Verification:

  • x = 15,000, so y = 40,000 − 15,000 = 25,000.

  • SP_Duo = (4/3)×15,000 = 20,000; SP_Galaxy = (4/5)×25,000 = 20,000. Total SP = 40,000 = total CP, so no net gain or loss.

Final answer: The cost price of the Samsung Duo is Rs. 15,000.

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