Multiple choice

A shopkeeper has two varieties of rice. The first variety costs Rs. 40 per kg and the second variety costs Rs. 65 per kg. In what ratio must he mix the two varieties so that by selling the mixture at Rs. 57.5 per kg, he can make a profit of 15%?

  1. 1 : 2

  2. 2 : 3

  3. 2 : 1

  4. 3 : 2

  5. 3 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Selling price = 57.5, Profit = 15%. Cost price of mixture = 57.5 / 1.15 = 50. Using alligation: (65 - 50) : (50 - 40) = 15 : 10 = 3 : 2.

AI explanation

First, find the cost price of the mixture by dividing the selling price of Rs. 57.5 by 1.15 to account for the 15% profit, yielding a cost price of Rs. 50 per kg. Using the rule of alligation with the Rs. 40 variety, the desired Rs. 50 mean price, and the Rs. 65 variety gives the ratio as (65 minus 50) to (50 minus 40). This simplifies to a ratio of 15 to 10, meaning the shopkeeper must mix the first and second varieties in a 3:2 ratio.

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