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.

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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.

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260+ Most Asked Ratio And Proportion Questions

61. If a : b = 2 : 3, a : d = 3 : 4, and e : d = 3 : 5, then e : b = ?

यदि a : b = 2 : 3, a : d = 3 : 4, और e : d = 3 : 5, तो e : b = ?


Option”C” is correct

⇒ a : d = 3 : 4 — (2) × 2

⇒ a : b : d = 6 : 9 : 8 — (3) × 5

⇒ e : d = 3 : 5 — (4) × 8

⇒ a : b : d : e = 30 : 45 : 40 : 24

⇒ e : b = 24 : 45 = 8 : 15

62. If x is increased by 30%, it becomes equal to ¾ times 260% of y. If x = 45369 then y = ?

यदि x के मान में 30% की वृद्धि कर दी जाये, तो यह y के 260% के ¾ के बराबर हो जायेगा| यदि x = 45369 है तब y = ?


Option”B” is correct

Given:

If x is increased by 30%, it becomes equal to ¾ times 260% of y

Calculation:

x × 130/100 = ¾ × y × 260/100                     

⇒ y = (2/3) × x

⇒ y = (2/3) × 45369 = 2 × 15123 = 30246

63. If a : b = 3 : 2, b : c = 2 : 1, c : d = 1/3 : 1/7 and d : e = 1/4 : 1/5 find a : b : c : d : e.

यदि a : b = 3 : 2 है, b : c = 2 : 1 है, c : d = 1/3 : 1/7 है और d : e = 1/4 : 1/5 है, तो a : b : c : d : e ज्ञात कीजिये।


Option”C” is correct

a : b = 3 : 2 now check which options satisfied this ratio

1) a : b = 100 : 75 = 4 : 3 not equal to 3 : 2

2) a : b = 100 : 30 = 10 : 3 not equal to 3 : 2

3) a : b = 105 : 70 = 21 : 14 = 3 : 2 which is equal to 3 : 2

4) a : b = 105 : 35 = 21 : 7 = 3 : 1 which is not equal to 3 : 2

hence option 3 is correct option

64. If the incomes of persons A and B are in the ratio 7: 5 and expenditure in the ratio 3: 2. If each one of them saves Rs R then find the income of A in terms of R?

यदि व्यक्तियों A और B की आय का अनुपात 7: 5 और व्यय का अनुपात 3: 2 है। यदि दोनों में से प्रत्येक R रुपये की बचत करता है, तो R के पदों में A की आय ज्ञात कीजिये।


Option”A” is correct

The incomes of A and B are in the ratio 7: 5 and expenditures in the ratio 3: 2.

Formula:

Income = savings + expenditure

Calculation:

Let the income of A and B be 7x and 5x and expenses be 3y and 2y

Since each one of them saves R that means their savings are equal:

Savings of A = Savings of B

7x – 3y = 5x – 2y

 ⇒ 2x = y

Now savings of A = 7x – 3y = R

7x – 3 × 2x = R

⇒ 7x – 6x = R

⇒ x = R

∴ income of A in terms of R = 7x = 7R

65. A person has divided his wealth among his son, daughter and wife in such a way that the wife received as much more amount as daughter as the daughter received more than the son. If son and wife together received Rs. 720000, then find the total amount of wealth.

एक व्यक्ति अपनी संपत्ति को अपने पुत्र, पुत्री और पत्नी के बीच इस प्रकार विभाजित करता है कि पत्नी, पुत्री से उतनी ही अधिक धनराशि प्राप्त करती है, जितनी पुत्री, पुत्र से अधिक प्राप्त करती है। यदि पुत्र और पत्नी एकत्रित रूप से 720000 रुपये प्राप्त करते हैं, तब संपत्ति की कुल धनराशि ज्ञात कीजिये।


Option”B” is correct

Given that the wife received as much more amount as daughter as the daughter received more than the son;

∴ Ratio of amount received by son, daughter and wife = x : (x + 1) : (x + 2)

∴ Amount received by daughter = (x + 1) / (3x + 3) = 1/3rd

∴ Son and wife together received 2/3rd of total amount.

Since son and wife together received Rs. 720000;

∴ Total amount = 720000 × 3/2 = Rs. 1080000

66. A person has sweets and chocolates in the ratio 8 : 13. He divided them among 26 children such that each child gets the sweets and chocolates in the ratio of 2 : 3. If 0 sweets and 13 chocolates are remaining after the distribution, then find the total number of sweets and chocolates.

एक व्यक्ति के पास मिठाई और चॉकलेट 8 : 13 के अनुपात में हैं। वह उसे 26 बच्चों के बीच इस प्रकार वितरित करता है कि प्रत्येक बच्चे को 2 : 3 के अनुपात में मिठाई और चॉकलेट प्राप्त होती है। यदि वितरण के बाद 0 मिठाई और 13 चॉकलेट शेष बचती हैं, तब मिठाइयों और चॉकलेटों की कुल संख्या ज्ञात कीजिये।


Option”C” is correct

Suppose the number of sweets and chocolates are 8x and 13x respectively.

He divided them among 26 children such that each child gets the sweets and chocolates in the ratio of 2 : 3;

∴ 26 × [2y + 3y] = [8x + 13x] – 13

⇒ 130y = 21x – 13

⇒ 21x – 130y = 13      —- (1)

Since no sweet is remaining:

26 × 2y = 8x

∴ x = 6.5y

From equation (1)

⇒ 136.5y – 130y = 13

⇒ y = 2

∴ x = 13

∴ Total number of sweets and chocolates = 13 × 21 = 273

67. The height of the two brothers is in the ratio of 13 ∶ 11. If the sum of their heights is 360 cm, find the height of the taller brother.

दो भाइयों की लम्बाई का अनुपात 13 ∶ 11 है। यदि उनकी लम्बाई का योग 360 सेमी. है, तो दोनों में से अधिक लम्बे भाई की लम्बाई ज्ञात कीजिये।


Option”D” is correct

The ratio of the height of two brothers = 13 : 11

Sum of their heights = 360

FORMULA USED:

Height of the taller brother

= (Ratio of taller brother / Sum of the ratio) × Sum of their heights

CALCULATION:

Sum of ratios = 13 + 11 = 24

∴ Height of the taller brother = (13/24) × 360 = 195 cm

68. A bag contains Rs.1, 50 paise and 25 paise coins. The no. of Total coins are 378 and the ratio of their value is 13 : 11 : 7; Find the sum of the number of 50 paise coins And 25 paise coins?

एक बैग में 1 रुपए, 50 पैसे और 25 पैसे के सिक्के हैं। कुल सिक्कों की संख्या 378 है और उनके मान का अनुपात 13 : 11 : 7 है। 50 पैसे और 25 पैसे के सिक्कों की कुल संख्या ज्ञात कीजिए।


Option”C” is correct

Total number of coins is 378

Rs. 1 : 50 paise : 25 paise coins is 13 : 11 : 7

Formula Used:

Total money = Number of coins × Value of each coin

Calculations:

Ratio of values of Rs. 1, 50 paise : 25 paise coins = 13 : 11 : 7

⇒ Ratio of number of Rs. 1, 50 paise : 25 paise coins = (13/1) : (11/(1/2)) : (7/( 1/4))

⇒ Ratio of number of Rs. 1, 50 paise : 25 paise coins = 13 : 22 : 28

Total number of coins = 378

⇒ 1 unit = 378/(13 + 22 + 28) = 6

Sum of number of 50 paise and 25 paise coins = (22 + 28) × 6

⇒ Sum of number of 50 paise and 25 paise coins = 300

∴ The sum of number of 50 paise and 25 paise coins is 300.

69. If (x + y – z) : (y – z + 2w) : (2x + z – w) = 2 : 3 : 1, then the ratio of (5w – 3x – z) : 3w = ?


Option”C” is correct

Given:

(x + y – z) : (y – z + 2w) : (2x + z – w) = 2 : 3 : 1

Calculation:

(x + y – z) : (y – z + 2w) : (2x + z – w) = 2 : 3 : 1

⇒ (x + y – z) + (2x + z – w) = (y – z + 2w)

⇒ 3x + y – w = y – z + 2w

⇒ – 3w = – 3x – z

Now,

(5w – 3x – z) : 3w

⇒ (5w – 3w) : 3w

⇒ 2w : 3w

⇒ 2 : 3

∴ Required ratio is 2 : 3

70. The marks of A are 90 more than that of C. The ratio of the difference between the marks of A and C and that of B and C is 5 ∶ 2 and the marks of B are more than that of C, then find the ratio of the difference between the marks of A and C to that of A and B?

A के अंक C के अंकों से 90 अधिक हैं। A और C के अंकों के बीच के अंतर और B और C के अंकों के बीच के अंतर का अनुपात 5 ∶ 2 है और B के अंक C के अंकों से अधिक हैं, तो A और C के अंकों बीच के अंतर और A और B के अंकों के बीच के अंतर का अनुपात ज्ञात कीजिए?


Option”C” is correct

Given that,

A – C = 90       —-(1)

From the question:

(A – C) / (B – C) = 5/2

90/(B – C) = 5/2

B – C = 36       —-(2)

From equation (1) and (2):

A – B + 36 = 90

A – B = 54

Required ratio = (A – C) ∶ (A – B) = 90 ∶ 54 = 5 ∶ 3