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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260+ Most Asked Ratio And Proportion Questions

81. In a cricket match, the ratio of runs scored by first four batsmen was 2 ∶ 3 ∶ 1 ∶ 5. Total 330 runs are scored in an inning and 80% of the runs are scored by top 4 batsmen only. How many half-centuries [Betwen 50 – 100 runs] are scored in that innings if the last batsman scored 18 runs?

एक क्रिकेट मैच में, पहले चार बल्लेबाजों द्वारा बनाये गए रनों का अनुपात 2 ∶ 3 ∶ 1 ∶ 5 था। एक पारी में कुल 330 रन बनाये गए और केवल शीर्ष 4 बल्लेबाजों द्वारा 80% रन बनाये गए। यदि अंतिम बल्लेबाज ने 18 रन बनाये तब उस पारी में कितने अर्द्ध-शतक [50 – 100 के बीच रन] बनाए गए?


Option”C” is correct

Total 330 runs are scored in an inning and 80% of the runs are scored by top 4 batsman only

So, total score of top 4 batsmen = 330 × 0.8 = 264

Since the ratio of runs scored by first four batsmen was 2 ∶ 3 ∶ 1 ∶ 5;

So, their respective scores are∶ 48, 72, 24, 120

Since the last batsman scored 18 runs,

Remaining score = 330 – 264 – 18 = 48

Hence, only 2nd batsman scored half-century, fourth batsmen century.

∴ Total half-centuries scored in that innings = 1

82. If unit place digit and tenth place digit of a two-digit number are in the ratio 1 : 2 and the difference between the tenth-place digit and the unit place digit is 4. Find the ratio of the two-digit number and number obtained by interchanging two digits.

यदि दो अंकों की संख्या का इकाई का अंक और दहाई अंक का अनुपात 1 : 2 है और दहाई अंक तथा इकाई अंक के मध्य अंतर 4 है। तब दो अंकों की संख्या और दो अंकों को परस्पर बदलने पर प्राप्त संख्या के मध्य का अनुपात ज्ञात कीजिये।


Option”C” is correct

Let the two-digit number be 10x + y where x and y are 10th place digit and unit place digit respectively.

Given,

⇒ x : y = 2 : 1

⇒ x = 2y

⇒ x – y = 4

⇒ y = 4

⇒ x = 8

Two-digit number = 8 × 10 + 4 = 84

Number after interchanging two digits = 48

Required ratio = 84 : 48

= 7 : 4

83. A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?

एक बैग में ₹ 2, ₹ 5 और ₹ 10 के सिक्कों के मूल्यवर्ग में ₹ 785 है। सिक्के 6 : 9 : 10 के अनुपात में हैं। बैग में ₹ 5 के कितने सिक्के हैं?


Option”C” is correct

Let the number of coins of ₹ 2, ₹ 5 and ₹ 10 be 6x, 9x, and 10x respectively

⇒ (2 × 6x) + (5 × 9x) + (10 × 10x) = 785

⇒ 157x = 785

∴ x = 5

Number of coins of 

₹ 5 = 9x = 9 × 5 =

∴ 45 coins of ₹ 5 are in the bag

84. In a 100 m race, A beats B by 10 m and B beats C by 10 m. By what distance does A beat C (in m)?

100 मीटर की एक दौड़ में, A, B को 10 मीटर से और B, C को 10 मीटर से परास्त कर देता है। A, C को कितनी दूरी (मीटर में) से परास्त करता है?


Option”B” is correct

Given:

In a 100 m race, A beats B by 10 m

And B beats C by 10 m

Solution:

According to question,

When A covers 100 m, B covers 90 m

And when B covers 100 m, C covers 90 m

⇒ Distance ratio of A to B and B to C are 10 : 9 and 10 : 9

⇒ A : B : C = 100 : 90 : 81

∴ A beats C by 19 m

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

Four friends A, B, C and D have some marbles with them. The ratio of the number of marbles with C and D is 7 : 6. B has one marble less than that with D. The ratio of the number of marbles with A and C is 12 : 7. Which of the following cannot be the total number of marbles with them?

निर्देश: दिए गए विकल्पों में से सही विकल्प का चयन कीजिए।

चार दोस्तों A, B, C और D के पास कुछ कंचे हैं। C और D के पास कंचों की संख्या का अनुपात 7 : 6 है। B के पास D से एक कंचा कम है। A और C के पास कंचों की संख्या का अनुपात 12 : 7 है। निम्न में से कौन सी उनके पास कुल कंचों की संख्या नहीं हो सकती है?


Option”D” is correct

Let the number of marbles with C and D be 7x and 6x respectively.

The number of marbles with B is 6x – 1.

The number of marbles with A is 12x.

Total number of marbles with them = 12x + 6x – 1 + 7x + 6x = 31x – 1

The number of marbles can be 30, 185, 309 when the value of x is 1, 6 and 10 respectively.

The total number of marbles cannot be 155.

86. A woman distributed her savings between her daughters A, B and C in the ratio 6 : 7 : 11. If B gives Rs. 700 from her share to A, the ratio of shares of A, B and C becomes 5 : 4 : 3. What is the average sum of shares (in Rs.) of A and B, in the beginning?

एक महिला ने अपनी बेटियों A, B और C के बीच अपनी बचत को 6: 7: 11. के अनुपात में वितरित किया। यदि B अपने हिस्से में से 700 रुपए A को देती है,तो A, B और C के हिस्से का अनुपात 5: 4: 3 हो जाता है। शुरुआत में A और B के हिस्सा का औसत योग (रुपये में) क्या है?


Option”D” is correct

Ratio of savings between her daughters A, B and C = 6 : 7 : 11

According to the question

(7x – 700)/(6x + 700) = 4/5

⇒ 35x – 3500 = 24x + 2800

⇒ 35x – 24x = 2800 + 3500

⇒ 11x = 6300

⇒ x = 6300/11

Share of A and B in the beginning = 6x + 7x = 13x = 13 × 6300/11 = 81900/11

Average sum of share of A and B = 81900/11 × ½ = 3722.72 ≈ 3722

87. The population of a town increased by 10% and 20% in two successive years, but decreased by 25% in the third year. Find the ratio of the population in the third year and the population 3 years back.

एक शहर की आबादी लगातार दो वर्षों में 10% और 20% बढ़ी, लेकिन तीसरे वर्ष में 25% घट गई। तीसरे वर्ष में जनसंख्या और 3 वर्ष पीछे की जनसंख्या का अनुपात ज्ञात कीजिए।


Option”B” is correct

Let the population of the town in the starting be 100

Population after 3 years = 100 × 110/100 × 120/100 × 75/100 = 99

Required ratio = 99 : 100

88. The third proportional to 9 and 15 is:

9 और 15 के लिए तीसरा आनुपातिक है:


Option”D” is correct

Let, the third proportional be x

Then,

9 : 15 : : 15 : x

⇒ 9/15 = 15/x

⇒ x = (15 × 15) / 9

⇒ x = 25

∴ The required third proportional to 9 and 15 is 25.

89. Rohit and Shikhar have their monthly incomes in the ratio of 9 : 7 while their monthly expenditures are in the ratio of 4 : 3, if they have saved Rs. 15000 and 12000 per months respectively, then the difference in their monthly income is

रोहित और शिखर की मासिक आय 9 : 7 के अनुपात में है, जबकि उनके मासिक व्यय 4 : 3 के अनुपात में हैं, यदि उन्होंने क्रमशः 15000 और 12000 रु महीने बचाया है, फिर उनकी मासिक आय में अंतर है


Option”A” is correct

Income ratio of Rohit and Shikhar = 9 : 7

Expenditure ratio of Rohit and Shikhar = 4 : 3

Savings of Rohit and Shikhar = 15000 and 12000 respectively

FORMULA USED:

Income – savings = Expenditure

CALCULATION:

Let the monthly income of Rohit and Shikhar be 9x and 7x respectively

According to the question,

(9x – 15000)/(7x – 12000) = 4/3

⇒ 27x – 45000 = 28x – 48000

⇒ x = 3000

Difference in Monthly Income = (9x – 7x) = 2 × 3000 = Rs. 6000

90. The ratio of Land And water on earth is 1 : 2 and the ratio of Land And water in Northern Hemisphere is 2 : 3. Find the ratio of Land to water in southern Hemisphere?

पृथ्वी पर भूमि और जल का अनुपात 1 : 2 है और उत्तरी गोलार्ध में भूमि और जल का अनुपात 2 : 3 हैI दक्षिणी गोलार्ध में भूमि : जल का अनुपात ज्ञात कीजिए?


Option”A” is correct

The ratio of Land And water on earth is 1 : 2 and the ratio of Land And water in the Northern Hemisphere is 2 : 3

Calculation:

Let the total area of the earth be 30 unit

So in the northern hemisphere area = 15 unit and in Southern hemisphere area = 15 unit

Total land = 1 × 30/3 = 10 unit

Total water = 2 × 30/3 = 20 unit

Land in the northern hemisphere = 2 × 15/5 = 6 unit

Water in the northern hemisphere = 3 × 15/5 = 9 unit

∴ The ratio of land and water in the southern hemisphere = (10 – 6) : (20 – 9) = 4 : 11