Ratio & Proportion Concepts and Shortcuts for RBI Grade B Exam

The Quantitative Aptitude section in RBI Grade B Phase 1 has 30 questions. Ratio & Proportion usually takes 2-3 of them. That’s 6–10% of the section. In short, it’s not a frequently asked topic in the Quantitative Aptitude section. So, on average, you can expect around 1 question from this topic. It is not as important as other topics like Number Series, Data Interpretation (DI), and Quadratic Equations. But you should not ignore it. And you should be prepared to quickly solve even if any question on this topic that appears in the exam. And you can do so, even if you understand the basics and apply the right shortcuts, you can solve these questions quickly and accurately. Ratio and Proportion questions are pure logic and calculation. In this blog, we will explain Ratio and Proportion in simple words, give you important formulas, and share smart shortcuts to save your time in the real exam.

ALSO READ: How to Score Maximum Marks in Cloze Test

Important Formulas To Know For Ratio & Proportion

Ratio & Proportion is one of the basic and must-know topics to start your RBI Grade B Phase 1 Quantitative Aptitude preparation. First, go through the table to get a quick overview of all the important Ratio & Proportion concepts with short explanations. Once you are clear with the basics, start practicing the questions given along with detailed solutions.

What is Ratio and Proportion?

A ratio compares quantities. That is to say, A:B = 2:3. It means, for every 2 parts of A, there are 3 parts of B. The meaning of proportion is that two ratios are equal. If 2:3 = 4:6, both show the same relationship. hence, in the exam, you may need to find a missing value, divide an amount in a ratio, or compare quantities fast.

Why Ratio and Proportion Matter for RBI Grade B Exam

Ratio & Proportion questions often appear in Data Interpretation, Simplification, and Word Problems. Many DI questions are based on ratio comparisons. So, mastering them helps in multiple areas. Why? Because, simple formulas save time. And this is important in Phase 1.

Basic Concepts You Must Know

There are some basic concepts that one must be aware of to deal with all types of questions that pop up in the Quantitative Aptitude or Numerical Ability section of the RBI Grade B Phase 1 exam.

Here are the main concepts that you must master to master this topic:

1. Ratio Formula: Ratio = Quantity 1 / Quantity 2 (written as a : b)

2. Proportion Formula: If a:b = c:d, then a × d = b × c (cross multiplication rule).

3. Finding a Third Quantity: If a:b = m:n and b:c = p:q, then a:c = m×p : n×q.

4. Dividing an Amount in a Ratio: If a sum S is to be divided in the ratio m:n:

• Share of first = (m / total parts) × S
• Share of second = (n / total parts) × S

Example 1: Simple Ratio

Let’s assume that the ratio of boys to girls is 3:2. And there are 60 students in total, then,
Parts = 3+2 = 5
Boys = (3/5)×60 = 36
Girls = (2/5)×60 = 24

Example 2: Using Proportion

If 5 pens cost Rs. 50, how much will 8 pens cost?
5:50 = 8:x
Cross-multiply: 5x = 8×50
x = Rs. 80

ALSO READ: How to Score Maximum Marks in Cloze Test & Ratio & Proportion Concepts and Shortcuts for RBI Grade B Exam

Types of Questions Asked in RBI Grade B

Here are the kinds of questions that you need to prepare:

1. Simple Ratio Problems: Direct ratio comparison or distribution. Usually very fast to solve.

2. Proportion and Missing Value: These require cross multiplication to find the missing term.

3. Compound Ratio: Combining two or more ratios.

For, example: If A:B = 2:3 and B:C = 4:5, then A:C = 2×4 : 3×5 = 8:15.

4. Partnership Problems: Based on investment ratios and time periods.

For example, A invests Rs. 5000 for 12 months, B invests rs. 8000 for 6 months. Profit share ratio = (5000×12):(8000×6) = 60000:48000 = 5:4.

5. Speed, Time, and Work Related Ratios: Many application-based word problems involve converting given conditions into ratios.

Shortcuts for Ratio and Proportion

Shortcuts play an important role in solving such questions quickly. Let’s talk about the shortcuts with practical examples so you can understand and apply them well. There are 5 shortcuts in this regard. They are Ratio Scaling, Reverse Ratio, Direct Proportion, Inverse Proportion, and Equalizing Ratios.

Check out the table below to know them well:

Tips to Solve Ratio and Proportion Quickly

Here are some simple tips to follow to make sure you know well how to answer Ratio and Proportion questions:

Tip 1: Learn by heart the common fraction-to-ratio conversions: Example: 1/2 = 1:2, 2/3 = 2:3, 3/4 = 3:4. Saves time in DI sets.

Tip 2: Read the question carefully: Many ratio questions hide “total” values or changes in quantity.

Tip 3: Practise with word problems: Partnership, speed-time-distance, and mixture problems often use ratio basics.

Tip 4: Avoid unnecessary steps: Use mental math wherever possible.

Tip 5: Use mock tests for timing practice: Ratio questions are fast, but only if you’ve practised enough to avoid re-calculation.

Practice Time

Question: A sum of ₹720 is divided between A, B, C in the ratio 2:3:4. Find each share.

Total parts = 2+3+4 = 9

A = (2/9)×720 = Rs. 160

B = (3/9)×720 = Rs. 240

C = (4/9)×720 = Rs. 320

Question: If 3 kg of apples cost Rs. 180, how much will 5 kg cost?

3:180 = 5:x

3x = 900 becomes x = ₹300

Maintain a Mini Notebook

Just like you might do for Simplification or DI formulas, keep a small notebook for Ratio & Proportion. Write down:

• Important formulas
• Shortcuts that save time
• Your common mistakes
• Difficult examples solved step-by-step

Review it for 10 minutes daily before practice.

Where to Practise

• RBI Grade B mock tests
• Topic-wise quizzes in online test series
• Previous years’ question papers

Daily Mini Task

• Solve 5 ratio questions
• 2 word problems from partnership/mixture
• Revise one shortcut
• Note one difficult example

Repeat it for 10 to 15 days, and you can master Ratio & Proportion.

ALSO READ: Word Swap Tricks for RBI Grade B Phase 1 Exam

Questions For Ratio & Proportion For RBI Grade B Exam

Candidates should start preparing for Ratio & Proportion For RBI Grade B Exam with a list of questions provided in this section. We provided questions with detailed solutions for the convenience of candidates to improve their performance in RBI Grade B Phase 1 Exam 2024.

Question 1: After 8 years, the ratio of age of A to B will be 6:7. Age of B, 8 years ago was 20% more than age of A, 7 years ago. If the present average age of A, B, and C is 58 years then find the ratio of the age of A after 18 years to the present age of C.

A) 6:7

B) 7:6

C) 4:5

D) 5:4

E) None of these

Question 2: There are two friends A and B, and the ratio of the incomes of A to B is 7:12. A invests 20% of the salary in mutual funds and spends remaining amount. B invests 30% of the income in mutual fund and spends remaining amount. If the total amount that A and B spend is Rs. 28000, find the income of A.

A) Rs. 10000

B) Rs. 12000

C) Rs. 14000

D) Rs. 18000

E) Rs. 16000

Question 3: Ratio of age of Ramesh and Suresh after 8 years is 7:5 respectively. Age of Mukesh after 15 years will be 150% more than age of Suresh, eight years ago. If present average age of Ramesh and Mukesh is 46.5 years then find present age of Suresh.

A) 48 years

B) 45 years

C) 36 years

D) 32 years

E) 40 years

Question 4: Arun bought ‘x + 12’ kg of rice at Rs. ‘x + 24’ per kg and ‘x’ kg of pulse at Rs. ‘x + 34’ per kg. He mixed them together and sold the resulting mixture at a rate of Rs. 65 per kg. By doing so he made a profit of 25%. Find the value of x.

A) 20

B) 28

C) 24

D) 18

E) 16

Question 5: The ratio of present ages of ‘A’ and ‘B’ is 6:5, respectively. After 16 years, the ratio of their ages becomes 22:19, respectively. Find the ratio of their ages 12 years ago from now.

A) 6:5

B) 8:7

C) 3:2

D) 5:4

E) None of these

Solutions

Solution 1: B)

Let age of A and B after 8 years is 6x years and 7x years respectively.

According to question;

(7x – 16) = 1.2 × (6x – 15)

7x – 16 = 7.2x – 18

0.2x = 2

x = 10

Present age of A = 6 × 10 – 8 = 52 years

Present age of B = 7 × 10 – 8 = 62 years

Present age of C = 58 × 3 – 52 – 62 = 60 years

Desired ratio = (52 + 18):60 = 7:6

Hence, option b.

Solution 2: C)

Let the income of A = Rs. 7x

Income of B = Rs. 12x

As per the question,

7x × 80% + 12x × 70% = 28000

5.6x + 8.4x = 28000

14x = 28000

x = 2000

Income of A = 7x = Rs. 14000

Hence, option c.

Solution 3: D)

Let age of Ramesh and Suresh after 8 years will be 7x years and 5x years respectively.

Let present age of Mukesh is ‘y’ years.

According to question;

y + 15 = 2.5 × (5x – 16)

y + 15 = 12.5x – 40

y = 12.5x – 55………………………….(1)

And, (7x – 8 + y)/2 = 46.5

7x + y – 8 = 93

7x + y = 101

7x + 12.5x – 55 = 101 [From (1)]

19.5x = 156

x = 8

Present age of Suresh = 8 × 5 – 8 = 32 years

Hence, option d.

Solution 4: C)

Cost price of the mixture = 65/1.25 = Rs. 52 per kg

According to question;

(x + 12)(x + 24) + x(x + 34) = 52(x + 12 + x)

Or, x² + 36x + 288 + x² + 34x = 104x + 624

Or, 2x² – 34x – 336 = 0

Or, x² – 17x – 168 = 0

Or, x² – 24x + 7x – 168 = 0

Or, x(x – 24) + 7(x – 24) = 0

Or, (x – 24)(x + 7) = 0

Or, x = 24

Hence, option c.

Solution 5: D)

Let the present ages of ‘A’ and ‘B’ be 6x years and 5x years, respectively

According to the question,

(6x + 16)/(5x + 16) = 22/19

Or, 114x + 304 = 110x + 352

Or, 4x = 48

Or, x = 12

Therefore, age of ‘A’, 12 years ago from now = 6x – 12 = 60 years

Age of ‘B’, 12 years ago from now = 5x – 12 = 48 years

Required ratio = 60:48 = 5:4

Hence, option d.

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