Ratio and Proportion Questions

Multiple choice
  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Let original fares be 15x, 8x, 12x. After reduction, fares are 10x (1st reduced by 1/3) and 6x (2nd reduced by 1/4). With passenger ratio 3:7:9, let passengers be 3k, 7k, 9k. Total = 3k(10x) + 7k(6x) + 9k(12x) = 30kx + 42kx + 108kx = 180kx = 303600. First class collection = 30kx = 30/180 × 303600 = 50600. Quantity II: Let Ashish and Aman earn 7y and 4y. After changes, Ashish earns 8.75y, Aman earns 3.5y. New ratio Aman:Ashish = 3.5y:8.75y = 14:35 = 2:5, which matches given 5:2. Ashish's earning cannot be uniquely determined - any value of y satisfies the ratio.

Multiple choice
  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can't be established

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Aman:Bhanu = 3:4 and Bhanu:Chandan = 6:7. Converting to a common ratio gives Aman:Bhanu:Chandan = 9:12:14. Let their ages be 9x, 12x, 14x. After 3 years, average age = (9x+3 + 12x+3 + 14x+3)/3 = (35x+9)/3 = 20.5. Solving gives 35x = 52.5, so x = 1.5. Chandan's present age = 14×1.5 = 21 years. Quantity II: Bhanu:Chandan = 3:4, let ages be 3x, 4x. After 3 years: (3x+3)/(4x+3) = 7/9. Cross-multiplying: 27x + 27 = 28x + 21, giving x = 6. Bhanu's present age = 3×6 = 18 years. Since 21 > 18, Quantity I > Quantity II.

Multiple choice
  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I < Quantity II मात्रा I < मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or the relation cannot be established संबंध स्थापित नहीं किया जा सकता या मात्रा I = मात्रा II

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For Quantity I: Let P's age = 5x, Q's age = 7x. Using (5x-4)/(7x+10) = 1/2, we get x = 6, so P = 30. For Quantity II: Let P's age = 5x, Q's age = 8x. Using (5x+7)/(8x+7) = 2/3, we get x = 7, so P = 35. Since 30 < 35, Quantity I is less than Quantity II.

Multiple choice

Find the value of x and y from Q1 and Q2 and choose correct option. Q1 और Q2 से x और y का मान ज्ञात कीजिए और सही विकल्प चुनिए। Q1: ₹ 600000 is divided into three parts (the first part is ₹ x) in such a way that their respective amount; each at 10% interest; after 2 years, 4 years and 6 years respectively; is in the ratio of 12:21:32. ₹ 600000 को तीन भागों (पहला भाग ₹ x है) में इस प्रकार विभाजित किया गया कि उनका संगत मिश्रधन; प्रत्येक पर 10% प्रति वार्षिक की दर से; क्रमश: 2 साल, 4 साल और 6 साल के बाद 12:21:32 के अनुपात में हो जाता है. Q2: A man deposited ₹ 3480000 between his two sons in such a way that when they aged 18 years they could receive equal amounts. They aged 15 years and 13 years. If the rate of the interest is 4% pa. The difference of the amount of money deposited in their accounts is ₹ y. एक आदमी ने ₹ 3480000 अपने दो बेटों के खाते में इस प्रकार जमा कराता है कि वो अपने 18 वें जन्मदिन पर एक समान धनराशि प्राप्त करें. उनकी आयु 15 वर्ष और 13 वर्ष है; यदि ब्याज की दर 4% प्रति वर्ष हो तो उनके खाते में जमा राशि का अंतर ₹ y है।

  1. x > y

  2. x < y

  3. x ≤ y

  4. x ≥ y

  5. x = y or CND

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Q1: Amounts after 2, 4, 6 years at 10% are in ratio 12:21:32. Each principal P at 10% for t years becomes P(1 + 0.1t). Setting P1(1.2):P2(1.4):P3(1.6) = 12:21:32 and P1 + P2 + P3 = 600000, we get P1 (first part = x) = ₹160000. Q2: Son1 (age 15) has 3 years to 18, Son2 (age 13) has 5 years. Let amounts be A and B with A(1.04)^3 = B(1.04)^5, so B/A = 1/(1.04)^2 ≈ 0.9246. Also A + B = 3480000. Solving: A ≈ ₹1808400, B ≈ ₹1671600. Difference y = ₹136800. Since x (₹160000) > y (₹136800), option A is correct.

Multiple choice
  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I < Quantity II मात्रा I < मात्रा II

  3. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relation can not be established मात्रा I = मात्रा II या निर्धारित नहीं किया जा सकता

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Ratio 2:3:5, sum of parts = 10. Total = 1200, so each part = 120. Smallest = 240, largest = 600, sum = 840. Quantity II: Ratio 5:6:11, sum of parts = 22. Total = 1100, so each part = 50. Middle = 300, twice middle = 600. Since 840 > 600, Quantity I > Quantity II.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (Only quantity is to be considered) निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़ें और उसके आधार पर मात्रा I और मात्रा II की तुलना करें। (केवल मात्रा पर विचार किया जाना है|) The ratio of boys to girls in a school is 4: 5. If 45 students from the same school left in the same ratio and 40 new girls joined the school, then the ratio of boys to girls becomes 4:9. एक विद्यालय में लड़कों का लड़कियों से अनुपात 4: 5 है। यदि उसी स्कूल के 45 छात्रों उसी अनुपात में विद्यालय छोड़ देते है और 40 नई लड़कियां विद्यालय में शामिल हो जाती हैं, तो लड़कों का लड़कियों से अनुपात 4: 9 हो जाता है। Quantity I: What percentage of total students will be boys if 50% of the total number of boys leave the school? Quantity II: 30% मात्रा I: कुल छात्रों का कितना प्रतिशत लड़के होंगे यदि कुल लड़कों की संख्या का 50% स्कूल छोड़ देते है? मात्रा II: 30%

  1. Quantity: I > Quantity: II मात्रा: I> मात्रा: II

  2. Quantity: I ≥ Quantity: II मात्रा: I: मात्रा: II

  3. Quantity: I < Quantity: II मात्रा: I < मात्रा: II

  4. Quantity: II ≥ Quantity: I मात्रा: II ≥ मात्रा: I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है|

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial boys=4x, girls=5x. After 45 students leave in 4:5 ratio: 20 boys, 25 girls leave. Remaining: boys=4x-20, girls=5x-25+40=5x+15. New ratio (4x-20)/(5x+15)=4/9 gives x=15. Initial: 60 boys, 75 girls. After changes: 40 boys, 90 girls. If 50% boys leave: 20 boys remain out of 110 total = 18.18%. Since 18.18% < 30%, Quantity I < Quantity II.

Multiple choice
  1. Rs. 1200 1200 रुपये।

  2. Rs. 2860 2640 रुपये।

  3. Rs. 1800 1800 रुपये।

  4. Rs. 1500 1500 रुपये।

  5. Can’t be determined निर्धारित नहीं किया जा सकता

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

One year ago, Laxman:Gopal = 3:5. Laxman's salary ratio (last year:present) = 4:5, Gopal's = 2:3. Let last year's salaries be 3x and 5x. Present salaries: Laxman = 3x × 5/4 = 15x/4, Gopal = 5x × 3/2 = 15x/2. Total present = 15x/4 + 15x/2 = 15x/4 + 30x/4 = 45x/4 = 4290. So 45x = 17160, x = 381.33. Gopal's present salary = 15x/2 = 15 × 381.33/2 = Rs. 2860 (approximately). Wait, let me verify: 4290 × 4/45 = 381.33, 15 × 381.33/2 = 2860. Yes, correct. There's a typo in option B (shows 2640 in Hindi but answer is B).

Multiple choice
  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the prices be P and 1.5P. Discount on first = 0.15P, discount on second = 0.27P. Statement I: 0.12P = 12300 gives P = 102500 (sufficient). Statement II: 0.27P = 11589 gives P = 42900 (sufficient). Each statement alone is sufficient.

Multiple choice
  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio 2:5:8, let prices be 2x, 5x, 8x. Statement I: Average = 4000, so (2x+5x+8x)/3 = 4000, 15x = 12000, x = 800. Cheapest = 2 × 800 = Rs 1600. Statement II: Total = 4000, so 15x = 4000, x = 266.67, cheapest = Rs 533.33. The statements give different answers, but each is independently sufficient.

Multiple choice
  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements I and II together are sufficient, but neither statement alone is sufficient.

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II directly gives the ratio A:B as 3:2 and B:C as 2:1, which means A:B:C = 3:2:1. This completely determines the ratio of investments for all three persons. Statement I only gives A's contribution and the total, which doesn't establish the ratio between B and C. Therefore, statement II alone is sufficient while statement I is not.

Multiple choice
  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statements together are sufficient, but neither statement alone is sufficient.

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II alone is sufficient. Given Jiya's salary is Rs. 20,450 and Veenu:Jiya = 6:5, we can calculate Veenu's salary = (6/5) × 20,450 = Rs. 24,540. Statement I is redundant as it restates the ratio already given in the question.

Multiple choice
  1. rs. $750$
  2. Rs. $850$
  3. Rs.$ 1000$
  4. Rs. $1250$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the numbers of first-class and second-class passengers be 1 and 50 units. Their collections are proportional to 1 x 3 and 50 x 1, giving a ratio of 3:50. The second-class collection is 50/53 x 1325 = Rs. 1250.

Multiple choice
  1. $22000$
  2. $16500$
  3. $11000$
  4. $5500$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Income ratio 3x:4x. Expenditure ratio 5y:7y. Savings ratio 3:2. (3x-5y)/(4x-7y) = 3/2. 6x-10y = 12x-21y, so 6x = 11y. Also 3x-5y = 500. Substitute x = 11y/6: 3(11y/6) - 5y = 500. 5.5y - 5y = 500, so 0.5y = 500, y = 1000. Income of Y = 4x = 4 * (11 * 1000 / 6) = 22000.