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

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7 thoughts on “Ratio & Proportion Questions”

  4. Anonymous

    Nice application 👍👍 9
    Thank so much 🥰🥰
    Very helpful for my pripresion

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