Multiple choice

Each of Vimla and Priya purchased a pen for the same price and each of them both marked up the prices of the pens by ₹ 95. Vimla offered a discount of ₹ 40 followed by another discount of 25%. Priya offered a discount of 25% followed by a further discount of ₹ 40. If Vimla's profit percentage is equal to the loss percentage incurred by Priya, then find the cost price (in ₹) of the pen which was bought by them.

  1. 120

  2. 136

  3. 148

  4. 145
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP = x. Marked price = x + 95. Vimla: SP = (x+95 - 40) * 0.75 = (x+55) * 0.75 = 0.75x + 41.25. Profit = 0.75x + 41.25 - x = 41.25 - 0.25x. Profit % = (41.25 - 0.25x)/x. Priya: SP = (x+95) * 0.75 - 40 = 0.75x + 71.25 - 40 = 0.75x + 31.25. Loss = x - (0.75x + 31.25) = 0.25x - 31.25. Loss % = (0.25x - 31.25)/x. Equating profit % and loss %: 41.25 - 0.25x = 0.25x - 31.25. 0.5x = 72.5, x = 145.

AI explanation

Assuming a cost price of P, the selling prices for Vimla and Priya after their respective successive discounts are both 0.75(P + 95) - 40. Since Vimla's profit equals Priya's loss, this selling price must exactly match the cost price, leading to 0.75(P + 95) - 40 = P. Solving this linear equation yields 0.75P + 71.25 - 40 = P, meaning 0.25P = 31.25 and the cost price is 145.

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