Table of Contents
Welcome to our practice quiz on Alligation Alternate! This quiz is designed to help students understand the concept better through various questions, complete with solutions and detailed explanations. Let’s test your knowledge and improve your skills in solving alligation problems.
Understanding Alligation Alternate
Alligation alternate is a method used to find the ratio in which two or more ingredients at different prices should be mixed to achieve a mixture at a desired price. It simplifies complex problems involving mixtures and costs.
Practice Questions
Question 1
Two types of rice costing ₹40 and ₹50 per kg are mixed to get a mixture costing ₹45 per kg. Find the ratio in which the two types of rice are mixed.
Question 2
A merchant has two types of cloth costing ₹80 and ₹100 per meter. He wants to prepare a mixture costing ₹90 per meter. Find the ratio in which he should mix the two types of cloth.
Solutions and Explanations
Solution to Question 1
Using alligation alternate, the difference between the higher and the mean price is ₹50 – ₹45 = ₹5, and the difference between the lower and the mean price is ₹45 – ₹40 = ₹5. The ratio of rice types is inverse to these differences:
- Rice costing ₹40: ₹50 – ₹45 = 5
- Rice costing ₹50: ₹45 – ₹40 = 5
Since both differences are equal, the rice types are mixed in a 1:1 ratio.
Solution to Question 2
Calculate the differences:
- Cloth costing ₹80: ₹100 – ₹90 = ₹10
- Cloth costing ₹100: ₹90 – ₹80 = ₹10
Again, both differences are equal, so the cloths should be mixed in a 1:1 ratio to get the desired cost of ₹90 per meter.
Additional Practice Questions
Try solving these on your own to strengthen your understanding of alligation alternate:
- Cost of sugar: ₹30/kg, cost of jaggery: ₹20/kg, desired cost: ₹25/kg. Find the ratio.
- Cost of two types of paint: ₹150 and ₹200 per liter, mixture cost: ₹170 per liter. Find the ratio.
Remember, practice makes perfect! Keep practicing these problems to master the concept of alligation alternate.