# 260+ Most Asked Ratio And Proportion Questions [100% Free ]

260+ Most Asked Ratio And Proportion Questions : Navigating the landscape of mathematics, one often comes across the fundamental concepts of “ratio and proportion questions“. Grasping the understanding of these is crucial, as ratio and proportion are woven deeply into the fabric of our daily activities, from intricate business dealings to the simplicity of preparing a home-cooked meal. When you see fractions presented in the form ‘a:b’, you’re observing a ratio. Conversely, when two such ratios equate, they form a proportion. And these concepts aren’t just restricted to math; they find resonance in science too.

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## 260+ Most Asked Ratio And Proportion Questions

1. A box contain equal number of 1 rupee, 2 rupee and 5 rupee coins. If the total amount is Rs. 184, then how many coins of each type are there?

एक बॉक्स में 1 रुपये, 2 रुपये और 5 रुपये के सिक्कों की बराबर संख्या विद्यमान है। यदि कुल राशि 184 रुपए है, तो प्रत्येक प्रकार के कुल कितने सिक्के विद्यमान हैं?

Option”D” is correct

Let equal number of 1 rupee, 2 rupee and 5 rupee coins be x

So, (1 × x + 2 × x + 5 × x) = 184

⇒ 8x = 184

⇒ x = 23

So, number of coins is 23

2. A number was divided in the ratio 3 : 2. When 8 was added to each, the ratio changed to 7 : 5. The greater of the two numbers was:

एक संख्या को 3 : 2 के अनुपात में विभाजित किया गया था। जब 8 को प्रत्येक में जोड़ा गया, तो अनुपात 7 : 5 हो गया। दो संख्याओं में से बड़ी संख्या थी:

Option”A” is correct

Let number parts be 3a and 2a.

When 8 was added to each, the ratio changed to 7 : 5,

⇒ (3a + 8)/(2a + 8) = 7/5

⇒ 15a + 40 = 14a + 56

⇒ a = 16

∴ Greater of two numbers = 3 × 16 = 48

3. Ratio of bananas to oranges is 4 : 5. If bananas decreased in the ratio 5 : 4 and oranges increased in the ratio 4 : 5 . What will be the new ratio of bananas to oranges?

केले और संतरों का अनुपात 4 : 5 है। यदि केलों के अनुपात में 5 : 4 से कमी होती है और संतरों के अनुपात में 4 : 5 से वृद्धि होती है, तब केले और संतरों का नया अनुपात क्या होगा?

Option”D” is correct

Let the ratio of bananas to orange = 4x : 5x

According to the question

⇒ 4x × [4/5] : 5x × [5/4]

⇒ 64 : 125

4. What is the ratio of mean proportional between 1.8 and 3.2 and the third proportional of 5 and 3?

1.8 और 3.2 के माध्य अनुपात तथा 5 और 3 के तीसरे आनुपातिक के मध्य का अनुपात क्या है?

Option”B” is correct

Given,

Mean proportional 1.8 and 3.2 = (1.8 × 3.2)1/2 = 2.4

Third proportional of 5 and 3 = 9/5 = 1.8

Required Ratio = 2.4 ∶ 1.8 = 4 ∶ 3

5. Two numbers A and B are in the ratio 5 : 2, If 4 is added to each number then this ratio becomes 9 : 4. If 5 is subtracted from each of the original number, then the ratio of A and B will be:

दो संख्याएँ A और B, 5 : 2 के अनुपात में हैं। यदि प्रत्येक संख्या में 4 जोड़ा जाता है, तो यह अनुपात 9 : 4 बन जाता है। यदि प्रत्येक वास्तविक संख्या से 5 घटाया जाता है, तो A और B का अनुपात क्या होगा?

Option”A” is correct

Let the two numbers be 5x and 2x

When 4 is added to each number,

(5x + 4)/(2x + 4) = 9/4

⇒ 4(5x + 4) = 9(2x + 4)

⇒ 20x + 16 = 18x + 36

⇒ 20x – 18x = 36 – 16

⇒ 2x = 20

⇒ x = 10

The original number = 5x = 50 and 2x = 20

When 5 is subtracted from each number, the ratio = (50 – 5) : (20 – 5) = 45 : 15 = 3 : 1

6. Incomes of A and B are in the ratio 5 : 3 and their expenditures are in the ratio 9 : 5. If income of A is twice the expenditure of B, then what is the ratio of savings of A and B?

A और B की आय 5 : 3 के अनुपात में है और उनके व्यय 9 : 5 के अनुपात में हैं। यदि A की आय B के व्यय की दोगुनी है, तो A और B की बचत का अनुपात क्या है?

OptionA” is correct

Ratio of income of A and B = 5 : 3      …(1)

Ratio of expenditure of A and B = 9 : 5      …(2)

Since income of A is twice the expenditure of B

∴ Multiply eqn..(1) by 2

Now

Ratio of income of A and B = 10 : 6

Also Ratio of expenditure of A and B = 9 : 5

∴ Ratio of saving of A and B = 1 : 1

7. The ratio of the number of cows to the number of buffaloes in a farm of 600 animals is 5 : 7. When some more buffaloes join the farm the ratio of the number of cows to the number of buffaloes changes to 5 : 8. How many more buffaloes join the farm?

600 जंतुओं के एक फार्म में गायों की संख्या का भैंसों की संख्या से अनुपात 5 : 7 है। जब कुछ भैंसें फार्म में शामिल होती हैं, गायों की संख्या का भैसों की संख्या से अनुपात 5 : 8 हो जाता है। कितनी अतिरिक्त भैसें फार्म में शामिल होती हैं?

Option”B” is correct

Given:

Number of animals in a farm = 600

Initial ratio of cow and buffalo = 5 : 7

Formula used:

If the ratio of cow and buffalo is a : b then,

Number of cow = (a/a + b) × total animals

Number of buffalo = (b/a + b) × total animals

Calculation:

Number of cows = (5/12) × 600 = 250

Number of buffaloes = (7/12) × 600 = 350

Let the number of buffaloes that join the farm be x.

According to question:

250/(350 + x) = 5/8

⇒ 2000 = 1750 × 5x

⇒ 5x = 250

⇒ x = 50

∴ 50 more buffaloes join the farm

8. In a classroom initial ratio of boys and girls is 7 : 6. Further 4 new boys joined the class and 3 girls left the class then ratio becomes 4 : 3. Find the number of girls initially in the class.

किसी कक्षा में लड़के और लड़कियों का प्रारंभिक अनुपात 7 : 6 था। 4 नए लड़कों के जुड़नें और 3 लड़कियों के छोड़ने के बाद अनुपात 4 : 3 हो जाता है। प्रारंभ में कक्षा में लड़कियों की संख्या ज्ञात कीजिये।

Option”B” is correct

Ratio of number of boys and girls initially = 7 : 6

Let number of boys be 7x and number of girls  be 6x.

According to the question,

(7x + 4) / (6x – 3) = 4/3

21x + 12 = 24x – 12

3x = 24

x = 8

⇒ Number of girls initially in the class = 6x = 6 × 8 = 48

9. A, B and C are three numbers such that the (A + B + C) ∶ (A + B) ∶ (B + C) ∶ (A + C) = 17 ∶ 14 ∶ 8 ∶ 12. Find the ratio (A + B – C) ∶ (A – B + C) ∶(A – B – C).

A, B और C तीन संख्याएँ इस प्रकार हैं कि (A + B + C) ∶ (A + B) ∶ (B + C) ∶ (A + C) = 17 ∶ 14 ∶ 8 ∶ 12 । (A + B – C) ∶ (A – B + C) ∶ (A – B – C) का अनुपात ज्ञात कीजिए।

Option”D” is correct

Suppose,

⇒ (A + B + C) = 17x      —-(1)

⇒ (A + B) = 14x      —-(2)

⇒ (B + C) = 8x      —-(3)

⇒ (A + C) = 12x      —-(4)

Subtracting (2) from (1), we get,

⇒ A + B + C – (A + B) = 17x – 14x

⇒ C = 3x

Subtracting (3) from (1), we get,

⇒ A + B + C – (B + C) = 17x – 8x

⇒ A = 9x

Subtracting (4) from (1), we get,

⇒ A + B + C – (A + C) = 17x – 12x

⇒ B = 5x

Hence,

(A + B – C) ∶ (A – B + C) ∶ (A – B – C)

= (9x + 5x – 3x) ∶ (9x – 5x + 3x) ∶ (9x – 5x – 3x)

= 11x ∶ 7x ∶ x

= 11 ∶ 7 ∶ 1

∴ The ratio of (A + B – C) ∶ (A – B + C) ∶ (A – B – C) = 11 ∶ 7 ∶ 1.

10. The three numbers A, B, C are in the ratio 1/2 : 2/3 : 3/4. The different between greatest and smallest numbers is 21. The three numbers A, B and C respectively are:

तीन संख्याओं A, B, C का अनुपात 1/2: 2/3: 3/4 है। सबसे बड़ी और सबसे छोटी संख्याओं के बीच का अंतर 21 है। क्रमशः तीन नंबर A, B और C हैं:

Option”D” is correct

The ratio of A, B and C is = 1/2 : 2/3 : 3/4 = 12/2 : 24/3 : 36/4 = 6 : 8 : 9

9 – 6 = 3 unit = 21

1 unit = 21/3 = 7

6 unit = 7 × 6 = 42

8 unit = 7 × 8 = 56

9 unit = 7 × 9 = 63

The three number A, B and C are 42, 56 and 63.