Solving Ratio and Proportion Problems for SSC CGL Arithmetic Ability

Solving Ratio and Proportion Problems for SSC CGL Arithmetic Ability

Ratio and Proportion are essential concepts in arithmetic, widely tested in various competitive exams including the SSC CGL. These concepts involve comparing quantities and determining their relationships. This post will guide you through solving ratio and proportion problems with practical examples tailored for SSC CGL aspirants.

Understanding Ratio and Proportion

A ratio is a way to compare two quantities by division, expressing how many times one number contains another. A proportion states that two ratios are equal.

Example Problems and Solutions

Problem 1: Basic Ratio Calculation

Question: If ₹50 is to be divided between Priya and Rahul in the ratio 3:2, how much will each person get?

Solution:

1. Step 1: Add the parts of the ratio. Here, $3 + 2 = 5$ parts in total.
2. Step 2: Determine the value of one part. $\frac{₹50}{5} = ₹10$ .
3. Step 3: Multiply the value of one part by the number of parts each person gets. Priya gets $3 \times ₹10 = ₹30$ and Rahul gets $2 \times ₹10 = ₹20$ .

Conclusion: Priya receives ₹30, and Rahul receives ₹20.

Problem 2: Finding an Unknown in a Proportion

Question: If $\frac{3}{4} = \frac{x}{20}$ , find the value of $x$ .

Solution:

1. Step 1: Set up the proportion such that the unknown $x$ is on one side. Given $\frac{3}{4} = \frac{x}{20}$ .
2. Step 2: Solve for $x$ by cross-multiplying: $3 \times 20 = 4 \times x$ .
3. Step 3: Simplify and solve for $x$ : $60 = 4x$ ⇒ $x = \frac{60}{4} = 15$ .

Conclusion: The value of $x$ is 15.

Problem 3: Using Ratios to Solve Real-World Problems

Question: Anil and Sunil have some money in the ratio 4:3. If Anil has ₹400, how much money does Sunil have?

Solution:

1. Step 1: Understand that Anil’s share corresponds to 4 parts and Sunil’s to 3 parts.
2. Step 2: Determine the value of one part by relating Anil’s share to the ratio: Anil’s share of ₹400 corresponds to 4 parts, so one part is $\frac{₹400}{4} = ₹100$ .
3. Step 3: Calculate Sunil’s share by multiplying the value of one part by his number of parts: $₹100 \times 3 = ₹300$ .

Conclusion: Sunil has ₹300.

Additional Ratio and Proportion Problems for SSC CGL Preparation

Problem 1: A mixture of milk and water is in the ratio 7:3 in a 40 liter mixture. How much water should be added to change the ratio to 7:5?

Problem 2: In a classroom, the ratio of boys to girls is 5:4. If there are 20 boys, how many students are there in total?

Problem 3: The salaries of Aman and Bimal are in the ratio 2:3. If the salary of Aman is increased by ₹10,000 and that of Bimal by ₹6,000, the new ratio becomes 5:7. What are their original salaries?

Solutions to the Problems:

Solution to Problem 1:

1. Original mixture: Milk = 7 parts, Water = 3 parts, Total = 40 liters.
2. Original amount of water: 3 parts out of 10 parts of 40 liters = $\frac{3}{10} \times 40 = 12$ liters.
3. Desired ratio of water: 5 parts (new ratio milk to water is 7:5).
4. New total parts in the mixture: 7 (milk) + 5 (water) = 12 parts.
5. Since the milk remains unchanged, its quantity relative to the new total must be recalculated: $\frac{7}{12} \times \text{New Total Volume} = 28$ liters (as milk is unchanged at 28 liters).
6. Calculate the new total volume needed to maintain 28 liters of milk at 7 parts of 12: $\frac{28}{7} \times 12 = 48$ liters.
7. New amount of water needed: Total mixture – original milk = $48 – 28 = 20$ liters of water.
8. Additional water to add: New water required – original water = $20 – 12 = 8$ liters.

Conclusion: 8 liters of water should be added.

Solution to Problem 2:

1. Ratio of boys to girls: 5:4.
2. Total ratio parts: $5 + 4 = 9$ parts.
3. If 20 boys represent 5 parts, each part equals $\frac{20}{5} = 4$ students.
4. Total students: $9 \times 4 = 36$ students.

Conclusion: There are 36 students in the classroom.

Solution to Problem 3:

1. Let the original salaries of Aman and Bimal be $2x$ and $3x$ respectively .
2. New salaries after increment:
   • Aman: $2x + 10,000$
   • Bimal: $3x + 6,000$
3. New ratio is 5:7:
   $$\frac{2x + 10,000}{3x + 6,000} = \frac{5}{7}$$
4. Cross multiply to solve for $x$ :
   $$14x + 70,000 = 15x + 30,000 \Rightarrow x = 40,000$$
5. Original salaries:
   • Aman: $2x = 2 \times 40,000 = ₹80,000$
   • Bimal: $3x = 3 \times 40,000 = ₹120,000$

Conclusion: Aman’s original salary was ₹80,000, and Bimal’s was ₹120,000.

These problems and their detailed solutions offer a solid practice opportunity for mastering ratios and proportions, enhancing both problem-solving speed and accuracy for exams like the SSC CGL.