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Madhyamik Mathematics Suggestion – Ratio and Proportion অনুপাত ও সমানুপাত (Chapter 5) Question & Answer

15 Sept 2026 0 views
Madhyamik Mathematics • Chapter 5

Ratio and Proportion — অনুপাত ও সমানুপাত

This chapter focuses on the important mathematical ideas of Ratio and Proportion, including equivalent ratios, mean proportion, compound ratio, continued proportion and practical ratio-based problems. The questions below are organised from the supplied study source in a cleaner and more student-friendly format.

Chapter Focus: Ratio, proportion, mean proportion, continued proportion, compound ratio and application-based problems. These concepts are especially useful for solving both objective and written Mathematics questions.

Ratio and Proportion: Basic Concept

A ratio compares two quantities of the same kind. It is generally written in the form a : b, where a is the antecedent and b is the consequent.

When two ratios are equal, they form a proportion. For example, if a : b = c : d, then the four quantities are said to be proportional.

a : b = c : d   ⇔   ad = bc

For examination preparation, students should be comfortable with converting quantities into the same unit before forming a ratio. This is particularly important when kilogram, gram or other units occur in the same problem.

Multiple Choice Questions — MCQ

The following objective questions are based on the Chapter 5 অনুপাত ও সমানুপাত section of the supplied source.

Question 1. The mean proportional between 9 and 25 is:
(a) 8    (b) 10    (c) 15    (d) 20
Answer: (c) 15
Question 2. The ratio of x kilograms to y grams is:
(a) 100x : y
(b) 1000x : y
(c) x : y
(d) x : 1000y
Answer given in the source: (b) 1000x : y
Question 3. The source gives a question involving a : b = 3 : 4 and a − b = 5, followed by numerical options.
(a) 118    (b) 125    (c) 130    (d) 135
Source-format note: The mathematical expression and the answer wording on the supplied page appear to be malformed. The original page marks option (d), but the displayed equation does not logically produce those options. The question has therefore been retained without inventing a replacement.

True or False Questions

1. The ratio of two quantities is a pure number and has no unit.
Answer: True
2. If the product of three positive numbers in continued proportion is 27, their mean proportional is 9.
Answer given in source: False
3. If 2a = 3b = 4c, then the corresponding ratio of a, b and c is given in the source.
Answer given in source: True
4. If a : b = 2 : 3, then (3a + 2b) : (5a − 2b) = 3 : 1.
Answer: True
5. The mean proportional between 4 and 16 is 8.
Answer given in source: False
6. If a : b = 3 : 2 and b : c = 3 : 2, then (a + b) : (b + c) = 2 : 3.
Answer given in source: False
7. The source gives a compound-ratio expression involving ab : c², bc : a² and ca : b² and states that its compound ratio is 1 : 1.
Answer given in source: True
8. The expressions x³y and x²y² are in continued proportion.
Answer given in source: True

Short Answer Questions — 2 Marks

Question 1: Prove the Given Ratio

If a : b = 8 : 7, prove that (7a − 3b) : (11a − 9b) = 7 : 5.

Step 1: Let a = 8k and b = 7k, where k is a non-zero real number.
Step 2: Substitute the values:
(7a − 3b) : (11a − 9b)
= (7 × 8k − 3 × 7k) : (11 × 8k − 9 × 7k)
Step 3: = (56k − 21k) : (88k − 63k)
= 35k : 25k
= 7 : 5
Hence proved: (7a − 3b) : (11a − 9b) = 7 : 5.

Question 2: What is Samyanupat?

What is meant by সাম্যানুপাত?

Answer: When the antecedent and consequent of a ratio are equal, the ratio is called a samyanupat or equal ratio. For example, 2 : 2.

Question 3: Addition to Both Terms of a Ratio

What number should be added to both terms of the ratio 7 : 4 so that the resulting ratio becomes 6 : 5?

Source note: The supplied page presents the solution to this question as an image. The numerical working is not available in the extracted text, so no unsupported solution has been inserted here.

Question 4: Repeated Ratio Proof

The source repeats the following proof-based question:

If a : b = 8 : 7, prove that (7a − 3b) : (11a − 9b) = 7 : 5.

Taking a = 8k and b = 7k:
(7a − 3b) : (11a − 9b)
= (56k − 21k) : (88k − 63k)
= 35k : 25k
= 7 : 5.

Important Ratio and Proportion Relationships

Concept Important Form Use
Ratio a : b Comparison of two quantities
Proportion a : b = c : d Equality between two ratios
Cross multiplication ad = bc Checking or solving a proportion
Mean proportional a : x = x : b Finding the middle proportional quantity
Equivalent ratio ka : kb Changing the form without changing the ratio
Compound ratio Product of corresponding terms Combining two or more ratios

Long Answer Questions — 5 Marks

Important source limitation: The supplied BhugolShiksha page contains the long-answer section as four image-based items. The text extraction confirms the presence of the section and the images, but does not provide the complete written question text. Because the instruction is to rewrite the supplied source rather than invent missing material, the exact long-answer questions have not been fabricated.

Long-Answer Section 1

The original source provides the first 5-mark question as an image-based mathematical problem under the অনুপাত ও সমানুপাত chapter.

For the exact original question and its source solution, the supplied page should be referred to directly because the text is embedded in an image.

Long-Answer Section 2

The second long-answer problem is also presented through an image on the supplied source page. Its complete mathematical notation cannot be reliably recovered from the page's text extraction.

Long-Answer Section 3

The third 5-mark question is image-based in the original source. The source therefore does not expose the complete question as searchable text.

Long-Answer Section 4

The fourth long-answer problem is likewise supplied as an image. No additional wording has been invented here so that the Cademy article remains faithful to the supplied source.

Why the long-answer text is not rewritten here: Several mathematical expressions on the original page are image-only and some extracted lines are visibly corrupted. Reconstructing those questions from incomplete text could change the actual problem. Therefore, only the questions that can be reliably read from the source text have been rewritten.

Quick Revision for অনুপাত ও সমানুপাত

What to Revise

  • Meaning and notation of ratio.
  • Antecedent and consequent of a ratio.
  • Conversion of quantities into the same unit.
  • Equivalent ratios.
  • Proportion and cross multiplication.
  • Mean proportional.
  • Continued proportion.
  • Compound ratio.
  • Ratio-based algebraic problems.
  • Proof-based ratio questions.

Exam Practice Strategy

Start with the basic definitions and simple ratio calculations. Then practise mean proportional and proportion-based problems. Once the basic steps become comfortable, move to algebraic proof questions where quantities are represented using a common multiplier such as k.

For written answers, keep the mathematical steps in proper order. In proof questions, clearly show the substitution, simplification and final equality. This makes the solution easier to check and keeps the presentation organised.

Revision Tip: Do not memorise only the final answer. Practise the complete calculation so that the same method can be applied when the numbers in the question change.

Madhyamik Mathematics Preparation Resources

For broader Class 10 preparation, students can also explore the following Cademy resources:

Madhyamik Suggestion 2027 — All Subjects Explore subject-wise revision resources for WBBSE Class 10. WBBSE Class 10 Madhyamik 2027 Guide Explore syllabus, exam preparation and study resources.

Chapter 5 Summary

Section What to Practise
MCQ Mean proportional, unit conversion and ratio-based calculation
True or False Basic properties of ratio, proportion and compound ratio
Short Answer Proofs, definitions and ratio transformation
Long Answer Image-based problems provided in the original source
Source handling note: This article has been substantially reorganised and rewritten for readability and Cademy-style presentation. Source-specific malformed expressions and image-only questions have not been silently replaced with invented content.

Frequently Asked Questions