Multiple choice

The Cost Price (CP) per unit of products P and Q is in ratio 5 : 6 and the profit received on selling a unit, each of products P and Q is the same. What would be the Sale Price (SP) per unit (in Rs) of product P, if profit per unit of product P is 20% of SP per unit of product Q and equal to Rs. 3000?

  1. 13,000

  2. 13,500

  3. 13,200

  4. 13,800
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A Correct answer
Explanation

Profit per unit = 3000. Profit = 20% of SP(Q). 3000 = 0.2 * SP(Q) => SP(Q) = 15000. CP(P):CP(Q) = 5:6. Let CP(P)=5x, CP(Q)=6x. SP(Q) = CP(Q) + Profit = 6x + 3000 = 15000 => 6x = 12000 => x = 2000. CP(P) = 5 * 2000 = 10000. SP(P) = CP(P) + Profit = 10000 + 3000 = 13000.

AI explanation

Let the cost prices of products P and Q be 5x and 6x, and their respective selling prices be S1 and S2. Since the profit is the same and equals Rs. 3000, we have S1 minus 5x equals 3000 and S2 minus 6x equals 3000. The first equation gives S1 equals 5x plus 3000, and the second equation gives 6x equals S2 minus 3000. We are given that the profit of Rs. 3000 is 20 percent of S2, so S2 equals 3000 divided by 0.20, which is Rs. 15000. Substituting S2 into the second equation gives 6x equals 15000 minus 3000, so 6x equals 12000 and x equals 2000. The selling price of product P is 5x plus 3000, which is 10000 plus 3000, resulting in Rs. 13,000.

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