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

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.

Now, we know that students sometimes find themselves tangled in the web of ratio and proportion questions. That’s where we come in. If you’ve been on the hunt for “ratio and proportion questions with solutions pdf“, or perhaps “ratio and proportion questions in Hindi“, you’re in the right place. Moreover, for those aiming to ace competitive exams, we’re catering specifically to your needs. Be it “ratio and proportion SSC questions” or “ratio and proportion questions for bank exams“, we’ve got you covered. Perhaps you’re targeting aptitude tests? Our “ratio and proportion aptitude questions” section will be your guiding star.

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Our goal? To dispel any confusion and arm our readers with the clarity and knowledge needed to tackle ratio and proportion questions head-on. As we delve deeper into this article, you’ll discover an array of solved examples, and a revisit of previous year ratio and proportion questions, to fortify your understanding.

Remember, mastering ratio and proportion questions not only equips you for specific topics but also lays a strong foundation for all Arithmetic chapters. So, whether you’re preparing for SSC, SBI, RBI, or any state government exams, this is your one-stop solution hub. Happy learning!

260+ Most Asked Ratio And Proportion Questions

51. If 20% of A = 30% of B = 1/6 of C, then find A ∶ B ∶ C.

यदि A का 20% = B का 30% = C का 1/6, तो A ∶ B ∶ C ज्ञात कीजिए।

12 ∶ 15 ∶ 18
15 ∶ 10 ∶ 18
15 ∶ 12 ∶ 18
18 ∶ 10 ∶ 12

Option”B” is correct

20% of A = 30% of B = 1/6 of C

⇒ 20/100 × A = 30/100 × B = 1/6 × C

⇒ A/5 = 3B/10 = C/6

⇒ A ∶ B ∶ C = 5 ∶ 10/3 ∶ 6 = 15 ∶ 10 ∶ 18

∴ A ∶ B ∶ C is 15 ∶ 10 ∶ 18.

52. If (x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c, then find a ∶ b ∶ c.

यदि (x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 है और 2x = a + b + c है, तो a ∶ b ∶ c का मान होगा-

23 ∶ 21 ∶ 22
23 ∶ 22 ∶ 21
21 ∶ 22 ∶ 23
22 ∶ 23 ∶ 21

Option”B” is correct

(x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c,

⇒ (x – a) = (a + b + c) /2 – a = (b + c – a) /2 = 10 —- 1

⇒ (x – b) = (a + b + c) /2 – b = (a + c – b) /2 = 11 —- 2

⇒ (x – c) = (a + b + c) /2 – c = (a + b – c) /2 = 12 —- 3

From equation 2 and 3,

⇒ (a + c – b) = 22

⇒ (a + b – c) = 24

⇒ a = 23

Similarly, b = 22 and c = 21

∴ a ∶ b ∶ c = 23 ∶ 22 ∶ 21

53. x, y, and z are three positive numbers such that x > y > z. If the difference and the sum of x and y are in the ratio 1 ∶ 7 and that of y and z is in the ratio 1 ∶ 3, then find the ratio x ∶ z.

x, y और z तीन धनात्मक संख्याएँ हैं जिसमें कि x > y > z है। यदि x व y के अंतर और योग का अनुपात 1 : 7 है। इसी प्रकार y व z के अंतर और योग का अनुपात 1 : 3 है, तो x ∶ z का अनुपात ज्ञात कीजिए।

9 ∶ 4
8 ∶ 3
7 ∶ 2
6 ∶ 1

Option”B” is correct

Difference and sum of x and y are in ratio 1 ∶ 7,

⇒ (x – y)/(x + y) = 1/7

⇒ 7x – 7y = x + y

⇒ 6x = 8y

⇒ y = 3x/4 —-(1)

Also,

Difference and sum of y and z are in ratio 1 ∶ 3,

⇒ (y – z)/(y + z) = 1/3

⇒ 3y – 3z = y + z

⇒ 2y = 4z

⇒ y = 2z

Substituting from (1),

⇒ 3x/4 = 2z

⇒ x/z = 8/3

∴ Required ratio = x ∶ z = 8 ∶ 3

54. The ratio of apples, oranges and mangoes is 1/3 ∶ 1/5 ∶ 1/4. If 10% of apples, 25% of oranges and 30% of mangoes are sold, then find the remaining ratio of apples, oranges and mangoes.

सेब, संतरे और आमों का अनुपात 1/3 ∶ 1/5 ∶ 1/4 है। यदि 10% सेब, 25% संतरे और 30% आम बेचे जाते हैं, तो शेष सेब, संतरे और आमों का अनुपात ज्ञात कीजिए।

14 ∶ 6 ∶ 7
11 ∶ 6 ∶ 7
10 ∶ 6 ∶ 7
12 ∶ 6 ∶ 7

Option”D” is correct

Ratio of apples, oranges and mangoes = 1/3 ∶ 1/5 ∶ 1/4 = 60/3 ∶ 60/5 ∶ 60/4 = 20 ∶ 12 ∶ 15

Let the number of apples, oranges and mangoes be 200x, 120x and 150x.

According to the question

Remaining ratio of apples, oranges and mangoes = 200x × [90/100] ∶ 120x × [75/100] ∶ 150x × [70/100] = 180x ∶ 90x ∶ 105x = 12 ∶ 6 ∶ 7

55. There are a certain number of Rs. 10, Rs. 20 and Rs. 50 notes available in a box. The ratio of the number of notes of Rs. 10, Rs. 20 and Rs. 50 is 3 ∶ 4 ∶ 6. The total amount available in a box is Rs. 2460. The amount of Rs. 10 and Rs. 50 in a box is –

एक बॉक्स में 10 रूपए, 20 रूपए और 50 रूपए के कुछ नोट हैं। 10, 20 और 50 रूपए के नोटों का अनुपात 3 ∶ 4 ∶ 6 है। बॉक्स में कुल 2460 रूपए हैं। बॉक्स में 10 और 50 रूपए के नोटों की कुल राशि कितनी है –

Rs. 1980
Rs. 1250
Rs. 2300
Rs. 1760

Option”A” is correct

Let the number of notes of Rs. 10, Rs. 20 and Rs. 50 be 3a, 4a and 6a respectively.

Given,

⇒ 10 × 3a + 20 × 4a + 50 × 6a = 2460

⇒ 410a = 2460

⇒ a = 6

Number of notes of Rs. 10 = 3 × 6 = 18

Number of Notes of Rs. 20 = 4 × 6 = 24

Number of notes of Rs. 50 = 6 × 6 = 36

Required amount = 10 × 18 + 50 × 36 = Rs. 1980

56. The ratio of the incomes of A and B is 3 : 5, whereas the ratio of their expenditures is 4 : 7 respectively. If A and B save Rs. 16,000 and Rs. 26,000, respectively, then what is the difference (in Rs.) between their expenditures?

A और B की आय का अनुपात 3 : 5 है, जबकि उनके व्यय का अनुपात क्रमशः 4 : 7 है। यदि A और B क्रमशः 16,000 रुपये और 26,000 रुपये की बचत करते हैं, तो उनके व्यय के बीच अंतर (रुपये में) कितना है?

5000
6000
5400
6800

Option”B” is correct

Income ratio of A and B = 3x : 5x

Expenditure ratio of A and B = 4y : 7y

Savings of A = Rs. 16000

Savings of B = Rs. 26000

Concept used:

We will be using the concept of ratio.

Income = Expediuture + Saving

Calculation:

According to the question,

3x – 4y = 16000 —-(1)

5x – 7y = 26000 —-(2)

Subtract equation (1) from equation (2) after multiply by 5 in equation (1) and multiply by 3 in equation (2)

y = 2000

Difference between the expenditure are = 7y – 4y = 3y = 3 × 2000 = 6000

∴ The correct answer is 6000.

57. The ratio of tables and chairs in a room is 7 : 9. If there are 560 tables and chairs in the room, then what is the number of chairs ?

Option”A” is correct

Given

The ratio of table and chairs = 7 : 9

number of tables and chairs = 560

Concept Used:

Concept of ratio and proportion

Calculation Used

Let the number of table and chair be 7x and 9x ‘

Total number of chair and table = 560

Accordingly,

16x = 560

⇒ x = 35

Number of chair = 9x = 9 × 35 = 315

∴ The number of chair is 315

58. If P : Q = 5 : 2, then (2P – 3Q) : (3P – 5Q) is equal to:

यदि P: Q = 5: 2, तो (2P – 3Q): (3P – 5Q) किसके बराबर है:

5 : 6
2 : 7
4 : 5
3 : 4

Option”C” is correct

Given:

P : Q = 5 : 2

Calculation:

Suppose P = 5k, Q = 2k

⇒ (2P – 3Q) : (3P – 5Q) = 2(5k) – 3(2k) : 3(5k) – 5(2k)

= 10k – 6k : 15k – 10k

= 4k : 5k

= 4 : 5

59.Directions: Select the correct alternative from the given choices.

There are three employees – A, B and C in a department along with their boss. The ratio of the number of working days of A in a month to the number of non-working days of his boss in that month is 10 : 11. The total number of working days for B and C in that month is 43. The total number of days in that month is 30. The ratio of non-working days for C to the working days of B is 12 : 25. The ratio of working days of A and B is 4 : 5. Find the average of their non-working days.

निर्देश: दिए गए विकल्पों में से सही विकल्प का चयन कीजिए।
उनके विभाग में तीन कर्मचारी हैं – A, B और C, उनके बॉस के साथ। एक महीने में A के कार्य दिवसों की संख्या से उस महीने में उसके बॉस के गैर-कार्य दिवसों की संख्या का अनुपात 10 : 11. है। उस महीने में B और C के लिए कार्य दिवसों की कुल संख्या 43 है। उस महीने में दिनों की संख्या 30 है। C के लिए गैर-कार्य दिवसों से B के कार्य दिवसों का अनुपात 12 : 25 है। A और B के कार्य दिवसों का अनुपात 4 : 5 है। उनके गैर-कार्य दिवसों का औसत ज्ञात कीजिए।

49/3
49/4
50/4
51/4

Option”B” is correct

Let the number of working days of A, B, C and the boss be a, b, c and d respectively.

a/(30 – d) = 10/11

b + c = 43

(30 – c)/b = 12/25

[30 –(43 – b)]/b = 12/25

(b – 13)/b = 12/25

b = 25

c = 43 – b = 43 – 25 = 18

The ratio of working days of A and B is 4 : 5.

Hence, number of working days for A is 20.

a/(30 – d) = 10/11

d = 8

The working days for A, B, C and boss is 20, 25, 18 and 8 respectively.

Therefore, the non-working days for A, B, C and boss is 10, 5, 12 and 22 respectively.

The average is (10 + 5 + 12 + 22)/4 = 49/4

60. If l : m : n = 1 : 2 : 4, then $\sqrt{\frac{5 l^{2} + m^{2} + n^{2}}{l^{2}}}$ is equal to:

Option”D” is correct

⇒ l : m : n = 1 : 2 : 4

Now,

$\sqrt{\frac{5 l^{2} + m^{2} + n^{2}}{l^{2}}}$

$\Rightarrow \sqrt{\frac{5 \times 1^{2} + 2^{2} + 4^{2}}{1^{2}}}$

⇒ √(5 + 4 + 16)

⇒ √25

⇒ 5

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