Quantitative Aptitude

Ratio and Proportion

775 Questions
All Dividing a total in a given ratio 393 Income, expenditure, and equal-savings equations 117 Ratio changes with constant sum/difference 89 Combining ratios 72 Finding a missing term in a proportion 54 Direct, inverse, and power variation 29 Mean proportional 9 Compound, duplicate, and root ratios 8 Componendo and dividendo 2

Ratio and Proportion Questions

Multiple choice

Passage

Directions: Study the following information carefully and answer the question. The following table represents the number of different questions of aptitude generated by four different people. Person Total Questions Generated Approved Questions (%) Questions Yet to be Checked (%) A 400 30 40 B - 35 45 C 700 - 60 D 900 40 - Note: '-' represents missing data. Money earned by each person (Rs.) = (Number of questions approved × 70) - (Number of questions disapproved × 10)

Find the difference between the total amounts of money earned by A and B, if the ratio of the total number of questions generated by A to that generated by B is 2 : 3.

  1. Rs. 6100

  2. Rs. 6200

  3. Rs. 6300

  4. Rs. 6400

  5. Rs. 6500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A: 400 total, 30% approved = 120, 40% checked = 160. Disapproved = 400 - 120 - 160 = 120. Earnings A = 120*70 - 120*10 = 7200. Ratio A:B = 2:3, so B = 600 total. B: 35% approved = 210, 45% checked = 270. Disapproved = 600 - 210 - 270 = 120. Earnings B = 210*70 - 120*10 = 13500. Difference = 6300.

Multiple choice

Passage

Each of the following questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer नीचे दिए गए प्रत्येक प्रश्न में एक प्रश्न और उसके नीचे दो कथन क्रमांक I और II दिए गए हैं। आपको यह तय करना है कि कथनों में दिया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों को पढ़िए और उत्तर दीजिए

Find the value of ‘R’ 'R' का मान ज्ञात कीजिए Statement I: Satish invested Rs. 10000 at R% p.a. at C.I for 2 years and Rs. 8000 at R% P.a. at S.I for 4 years. He got same amount from both schemes. Statement II : Ratio between principal invested at R% p.a. at CI to interest earned after 2 years is 25: 11 कथन I: सतीश ने रु. 10000 R % प्रति वर्ष पर 2 साल के लिए चक्रवृद्धि ब्याज पर और रु 8000 R % प्रति वर्ष पर साधारण ब्याज पर 4 साल के लिए निवेश किया उन्हें दोनों योजनाओं से समान राशि मिली। कथन II: R% प्रति वर्ष पर निवेश किए गए मूलधन और २ वर्ष बाद अर्जित चक्रवृधि व्याज के बीच का अनुपात 25: 11 है।

  1. Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the questions कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन कथन II अकेले प्रश्नों का उत्तर देने के लिए पर्याप्त नहीं है

  2. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question. कथन II अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन केवल कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question. दोनों कथनों को मिलाकर प्रश्नों का उत्तर देना आवश्यक है, लेकिन इनमें से कोई भी कथन अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  4. Either statement I or statement II by itself is sufficient to answer the question. या तो कथन I या कथन II अपने आप में प्रश्न का
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: 10000(1 + R/100)² = 8000(1 + 4R/100). This simplifies to 125(1 + R/50 + R²/10000) = 100(1 + R/25), giving 125 + 2.5R + 0.0125R² = 100 + 5R, or 0.0125R² - 2.5R + 25 = 0, which solves to R = 20 or 200. Statement II: Principal:CI after 2 years = 25:11. If principal = 25P, CI = 11P, so amount = 36P. Thus 25P(1 + R/100)² = 36P, giving (1 + R/100)² = 36/25, so 1 + R/100 = 6/5, R = 20. Statement II alone gives unique R = 20, while Statement I gives two values. Either alone works since II is sufficient.

Multiple choice

Passage

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)

Quantity I : When 9864 is divided into two parts in the ratio of 5 : 13, then what will be the value of largest part? Quantity II : Suresh spends 65% of his monthly income. If his monthly income is Rs. 13000, then how much does he save?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I <Quantity II

  4. Quantity II ≥ Quantity I

  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: 9864 divided in ratio 5:13. Total parts = 5 + 13 = 18. Larger part = (13/18) × 9864 = 13 × 548 = 7124. Quantity II: Monthly income = Rs 13000. Savings = 35% of 13000 (since 65% is spent) = 0.35 × 13000 = Rs 4550. Since 7124 > 4550, Quantity I > Quantity II. Option A is correct.

Multiple choice

Passage

Bar graph given below show percentage distribution of total unsold cakes on five different days by a shop. Read the data carefully and answer the questions. (i) Total 200 cakes baked each day from Sunday to Thursday. (ii) Total unsold cakes on particular day will be sold next day. (iii) There are no unsold cakes carry forward on Sunday.

9/14th of total sold cakes on Tuesday each cake sold for Rs. X and rest of cakes each cake sold for Rs. Y. If ratio of value of X to that of Y is 2 : 3 and shop received total amount of Rs. 1716 for selling all cakes on Tuesday, then find the total amount received by shop for selling each cake for Rs. X?

  1. 819 Rs.

  2. 936 Rs.

  3. 750 Rs.

  4. 702 Rs.

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total cakes on Tuesday = T. 9/14 of T sold at Rs. X each, and (1 - 9/14) = 5/14 of T sold at Rs. Y each. Ratio X:Y = 2:3, so let X = 2k, Y = 3k. Total revenue = (9/14)T × X + (5/14)T × Y = 1716. Substituting: (9/14)T × 2k + (5/14)T × 3k = 1716. (18/14)Tk + (15/14)Tk = (33/14)Tk = 1716, Tk = 1714×14/33 = 728. Amount from X-cakes = (9/14)T × X = (9/14)T × 2k = (18/14)Tk = (18/14)×728 = 936.

Multiple choice

Passage

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I = Quantity II or the relationship cannot be established from the information given (5) If Quantity I ≤ Quantity II

Ravi took a loan of Rs. X from bank A and Rs. 2X from bank B, each for 2 years. Bank A charges simple interest per annum. Bank B charges compound interest per annum at the rate of 10% per annum. The respective ratio between the interest from bank A and that from bank B was 5 : 14. Quantity I: Rate of interest charged by bank A Quantity II: Rate of interest charged by bank C when Rs. 1600 is borrowed by Ravi for 3 years gives simple interest of Rs. 408

  1. (1)

  2. (2)

  3. (3)

  4. (4)

  5. (5)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Bank A interest = X * R * 2 / 100. Bank B interest = 2X * ((1.1)^2 - 1) = 2X * 0.21 = 0.42X. Ratio A:B = (0.02*X*R) / (0.42*X) = 5/14. (0.02*R)/0.42 = 5/14. R = (5 * 0.42) / (14 * 0.02) = 2.1 / 0.28 = 7.5%. Quantity II: 408 = 1600 * R * 3 / 100 => 408 = 48 * R => R = 8.5%. Since 7.5 < 8.5, Q1 < Q2.

Multiple choice

Passage

Directions: The following problem consists of a question followed by three statements (I), (II), and (III). You have to determine which statement(s) is/are sufficient /necessary to answer the question.

Three persons X, Y and Z did some work and shared the money among them but not equally. What was the share of X? I. The ratio of the shares of X and Z is 3 : 5, respectively. II. If X gives Rs. 500 from his share to Y, then Y and Z would have equal amount of money. III. X's share is less than Y's share.

  1. Only I and II

  2. Only II and III

  3. Only I and III

  4. Cannot be answered even by using all three statements

  5. All three statements
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives X:Z ratio. Statement II gives a relationship between Y and Z. Statement III gives an inequality. We have no total amount or absolute values for any share, so we cannot determine X's specific share.

Multiple choice

Passage

Directions : The following item contains a question and two statements I and II. You have to decide whether the data given in the statements is sufficient to answer the question. Read both statements and give your answer as given below: (1) If statement I alone is sufficient to answer the question, while statement II alone is not sufficient to answer the question. (2) If statement II alone is sufficient to answer the question, while statement I alone is not sufficient to answer the question. (3) If either statement I alone or II alone is sufficient to answer the question. (4) If both statements together do not suffice to answer the question.

The ratio of the salary of Satish to that of Anoop to that of Sandeep is 4 : 5 : 7. How much is Anoop's salary? I. The difference between Anoop and Sandeep's salary is double that of Satish and Anoop. II. Anoop gets Rs. 4,000 less than Sandeep.

  1. 1

  2. 2

  3. 3

  4. 4

  5. e
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I: (A-S) = 2(S-A) implies A=S, which is impossible given the ratio. Statement II: A = S - 4000. Using the ratio 4:5:7, A=5x, S=7x. 7x - 5x = 4000, so 2x = 4000, x = 2000. Anoop's salary = 5 * 2000 = 10,000. Statement II alone is sufficient.

Multiple choice

Passage

Directions: The following table shows the total number of workers in different months of the year 2019 in a factory and the percentage of female workers. Male workers work only on weekdays and female workers work only on weekends. Month Number of workers Percentage of female workers January 1100 40% February 1280 15% March 1400 25% Note: 1 st January 2019 was a Tuesday. Weekdays include Monday, Tuesday, Wednesday, Thursday and Friday. Weekends include Saturday and Sunday. Working hours during weekdays are 8 hours/day and during weekends they are 10 hours/day. Total working hours = Total number of males/females worked × Number of days × Number of hours

If the wage on weekdays is Rs. 50/hour and the wage on weekends is Rs. 80/hours, then what will be the ratio of the total amount of wages given to men to that given to women in the month of March?

  1. 13 : 5

  2. 47 : 15

  3. 63 : 20

  4. 65 : 22

  5. 71 : 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: There was a football tournament between three teams: P, Q, and R. Each team played two matches. The scoring and penalty system was as follows: (i) Each team earns two points for every goal scored against the opponent. (ii) A team earns one extra point if a goal is scored from outside the D area. (iii) A team loses one point for each goal it concedes (i.e., a goal scored by the opponent). (iv) Only three players from each team scored goals in the tournament. Match 1: P vs Q ● Q won the match and earned 5 points. ● Team P scored 3 goals against Q. ● No player from Team P scored a goal from outside the D area. Match 2: P vs R ● R lost the match and earned zero points against P. ● Team P scored 2 goals, and one of them was from outside the D area. Match 3: Q vs R ● Team R scored one more goal than Team Q in this match. ● One player from Team Q scored a goal from outside the D area. Q earned 7 points from this match.

If the third-ranked team received ₹72,000 as prize money and the ratio of prize money for the first, second, and third-ranked teams was 9 : 6 : 4, then which of the following is correct?

  1. Prize money of team Q is more than ₹1,50,000

  2. Difference between the prize money received by Team P and Team Q is equal to the prize money received by Team R

  3. None of these

  4. Both options (1) and (2)

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer