SBI Clerk Mains Mock 2: Math Problem Solving Guide

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Hey guys! Let's dive into a common math problem you might face in the SBI Clerk Mains exam. We'll break down question number 37 from Mock 2, focusing on a mixture problem involving milk and water. The goal is not just to get the answer, but to understand the logic behind the solution, so you can tackle similar problems with confidence. This guide will help you build a solid foundation, ensuring you're well-prepared for the exam. Let's get started!

The Problem: Unveiling the Mixture Mystery

Alright, let's break down the problem statement step-by-step. The original problem presents a mixture containing milk and water, and the core challenge is to unravel the mathematical relationship within this mixture. Let's restate the question to ensure understanding: A mixture initially has milk and water in a specific ratio. Then, the scenario introduces changes: more water and milk are added. The ratio changes again! Finally, a portion of the mixture is removed, which leads us to the final question about how much milk and water remains. This type of problem is designed to test your ability to work with ratios, solve equations, and apply logical reasoning. The key to solving these types of problems lies in a systematic approach. You've got to break the problem down into manageable steps and use the information provided to formulate equations and find the unknowns. Keep in mind that understanding the fundamentals of ratio and proportion is super important here, and also the ability to set up and solve algebraic equations. This problem, like many others in the SBI Clerk Mains, tests your speed and accuracy so it's super important to practice regularly, so you can do these calculations quickly and efficiently. Time management is crucial, so try to solve these types of problems in a timely manner. We'll show you how to do it efficiently.

Problem Statement

A mixture contains water and milk in the ratio of 2:3. If 'a + 20' liters of water and 'a' liters of milk are added to it, the ratio becomes 7:8. If half of the mixture is removed, then the remaining mixture, the milk exceeds water by 10 liters. Find the initial quantity of the mixture.

Now, let's see how we can solve this problem. We'll use a step-by-step approach to make things super clear.

Step-by-Step Solution: Cracking the Code

Step 1: Initial Ratio and Variables

First, let's represent the initial quantities of water and milk using variables. Since the ratio of water to milk is 2:3, we can say:

  • Water = 2x liters
  • Milk = 3x liters

This makes it easier to work with the ratios and helps us set up equations.

Step 2: Adding Water and Milk

Next, the problem tells us that we add (a + 20) liters of water and 'a' liters of milk. So, the new quantities become:

  • New Water = 2x + (a + 20) liters
  • New Milk = 3x + a liters

Step 3: The New Ratio

After adding the water and milk, the ratio of water to milk changes to 7:8. We can write this as an equation:

(2x + a + 20) / (3x + a) = 7/8

Step 4: Solving for 'a' and 'x'

Let's solve the equation from Step 3 to find the values of 'a' and 'x'. Cross-multiplying, we get:

8 * (2x + a + 20) = 7 * (3x + a) 16x + 8a + 160 = 21x + 7a 5x - a = 160

Step 5: Removing Half the Mixture

At this point, we need to consider that half of the mixture is removed. However, to solve this problem, we're given the final condition which helps us establish a relationship between the final amounts of milk and water. When half of the mixture is removed, the remaining mixture, the milk exceeds the water by 10 liters.

(3x + a)/2 - (2x + a + 20)/2 = 10

(3x + a) - (2x + a + 20) = 20

x - 20 = 20

x = 40

Step 6: Finding the Value of 'a'

Now that we know x = 40. From step 4. we had: 5x - a = 160. Substitute the value of x.

5 * 40 - a = 160 200 - a = 160 a = 40

Step 7: Calculating the Initial Quantities

Now that we know x = 40, we can find the initial quantities of water and milk.

  • Initial Water = 2x = 2 * 40 = 80 liters
  • Initial Milk = 3x = 3 * 40 = 120 liters

Step 8: Calculate the Original Mixture

The original mixture has a total of 80 + 120 = 200 liters.

Final Answer: The Initial Mixture

So, the initial quantity of the mixture was 200 liters.

Key Takeaways: Mastering Mixture Problems

Ratio Fundamentals

This problem heavily relies on understanding ratios. Remember that ratios represent the relative proportions of different components in a mixture. Mastering ratio concepts is really important.

Setting Up Equations

Translating the word problem into mathematical equations is super important. The ability to correctly set up equations based on the information provided is the core of solving this problem type. You have to carefully analyze each sentence and figure out how to represent the information with mathematical expressions.

Step-by-Step Approach

Breaking the problem down into smaller, manageable steps makes the solution process much easier. Take it one step at a time! This helps avoid confusion and ensures you don't miss any crucial details.

Practice Makes Perfect

Practice is your best friend. The more mixture problems you solve, the more comfortable you'll become with the concepts and the faster you'll be at solving them. So, go on and find other similar problems to solve.

Time Management

During the SBI Clerk Mains exam, time is a crucial factor. Practicing these problems will help you solve them quickly and accurately. Try to set time limits for yourself when practicing, so you can improve your speed. Effective time management can significantly boost your score.

Additional Tips for the Exam

  • Read the question carefully: Make sure you understand what the problem is asking before you start solving it. Avoid making assumptions.
  • Draw diagrams: For problems that involve physical quantities or movements, diagrams can be very helpful to visualize the situation.
  • Check your work: Always double-check your calculations to avoid silly mistakes. A small error can mess up the entire solution.
  • Stay calm: It's common to feel stressed during an exam, but staying calm helps you think clearly. Take a deep breath and stay focused.

Conclusion: Your Path to Success

So there you have it! We've successfully solved the SBI Clerk Mains Mock 2 question. Remember that the key to success is understanding the underlying concepts, practicing regularly, and managing your time effectively. Keep working hard, stay focused, and you'll be well on your way to acing the SBI Clerk Mains exam. Good luck with your preparation, guys! Keep up the hard work, and you'll surely succeed. Don't be afraid to ask for help or seek guidance from mentors. You got this!

I hope this helps you with your preparation. Do not hesitate to ask if you have any questions or doubts. Keep up the amazing work! You will ace the exam for sure!