Multiple choice

Passage

Directions : Study the given information carefully and answer the question that follows. A bakery produces five cakes — Alpha, Beta, Gamma, Delta, and Epsilon. The cost price and selling price of each cake are among Rs. 400, Rs. 450, Rs. 500, Rs. 550, and Rs. 600. The cost price and the selling price of each cake is different. For any cake, the selling price is not equal to its cost price. (i) The cost price of Gamma is equal to the selling price of Delta. The bakery incurred a loss while selling Gamma, but earned a profit by selling Delta. (ii) The cost price of Beta is the average of Epsilon's cost price and selling price, and the bakery obtained a profit by selling Beta. (iii) The profit made by selling any cake is less than Rs. 200. The profit made on any two cakes is not the same. The loss incurred on any two cakes is not the same. (iv) Alpha was one of only three cakes that yielded a profit. The loss made on any cake is not Rs. 150. (v) Delta achieved the highest profit, whereas Epsilon incurred the maximum possible loss.

What is the difference (in Rs.) between the cost price and the selling price of Gamma?

  1. 50

  2. 100

  3. 150

  4. 200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Based on the constraints: Gamma cost = Delta selling. Profit/loss logic and unique values lead to the cost and selling price differences. Through systematic deduction of the price set (400, 450, 500, 550, 600), the difference for Gamma is 100.

AI explanation

The cost price and selling price values are 400, 450, 500, 550, and 600, and the profit or loss for any cake must be a multiple of 50, ranging from 50 to 200. Since Epsilon incurs the maximum possible loss, which must be less than 200 and not 150, Epsilon's loss is 100, making its cost price 500 and selling price 400, or cost price 600 and selling price 400 is not allowed since the maximum loss is 200. Delta achieves the highest profit, so Delta's profit is 150, meaning its selling price minus cost price equals 150, making the cost price 400 and selling price 550. Since the cost price of Gamma equals the selling price of Delta, Gamma's cost price is 550. Because Gamma incurs a loss, its selling price must be less than 550, and the only available price that creates a unique loss not already used is 450, resulting in a difference of 100. The result is 100.

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