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

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. The ratio of the cost price of article A to that of article B is 5 : 3. What is the profit percentage on article B? 1. The ratio of the selling price of article A to that of article B is 4 : 7. 2. The difference between the cost prices of articles A and B is Rs. 200 and the difference between the selling prices of articles B and A is Rs. 300.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP_A = 5x, CP_B = 3x. Statement 1 gives SP_A/SP_B = 4/7. We cannot find the profit percentage without knowing the absolute values. Statement 2 gives CP_A - CP_B = 2x = 200, so x = 100. CP_A = 500, CP_B = 300. SP_B - SP_A = 300. We have two variables (SP_A, SP_B) and one equation. Combining both, we have ratios and differences, which is sufficient.

Multiple choice

Shivi visited an fbb store. She purchased T-shirts and short-pants in the ratio of 4 : 3 during her first visit on 1st March, 2022 and paid Rs. 1,360 at the cash counter. During her second visit on 15th March, 2022, she purchased T-shirts and short-pants in the ratio of 3 : 1 and paid Rs. 1,080. The cost of a T-shirt, as well as a short-pant in rupees, is a positive integer. If Shivi purchased three short-pants on 15th March, 2022 which is equal to the half the number of short-pants purchased on 1st March, 2022, then the amount she paid in rupees for short-pants during second visit on 15th March, 2022 is ________.

  1. 80

  2. 120

  3. 360

  4. 450

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

In a tech startup in Bangalore, Ayan, Bhavya, Chetna, and Dhruv are close friends and colleagues with varying monthly salaries. Their monthly salary dynamics create an intriguing scenario: Ayan and Bhavya together earn in a month the equivalent of what Chetna earns in 9 months. Conversely, Chetna and Ayan together earn in a month what Bhavya earns in just 3 months. Dhruv, the fourth friend, earns in a month that is twice the amount Ayan earns monthly. Determine the ratio between the highest and lowest monthly salaries among Ayan, Bhavya, Chetna, and Dhruv.

  1. 13 : 1

  2. 17 : 4

  3. 13 : 3

  4. 12 : 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C, D be the salaries. Equations: A+B = 9C; C+A = 3B; D = 2A. From C+A=3B, C=3B-A. Substitute into A+B=9(3B-A) -> A+B = 27B-9A -> 10A = 26B -> A = 2.6B. Then C = 3B - 2.6B = 0.4B. D = 2A = 5.2B. Salaries are A=2.6B, B=B, C=0.4B, D=5.2B. Ratio of highest (D=5.2B) to lowest (C=0.4B) is 5.2/0.4 = 13/1.

Multiple choice

Directions: In the question below, the question is followed by five options. Read the information given in each option carefully and determine which of the following options, alone, is sufficient to find the answer. A farmer sold 6 bags of wheat and 9 bags of rice in a day. Determine the ratio of the cost price of one bag of wheat to one bag of rice (assuming the quantity of one rice bag is the same as that of one wheat bag).

  1. If all the items are sold at the cost price of a wheat bag, the farmer earns a 30% profit.

  2. If all the items are sold at the cost price of a rice bag, the farmer incurs a 15% loss.

  3. The ratio of the total cost price of 6 bags of wheat to 9 bags of rice is 5 : 4.

  4. The difference between the cost prices of one bag of wheat and one bag of rice is Rs. 250.

  5. The sum of the cost prices of one bag of wheat and one bag of rice is Rs. 850, and the total cost price of all items sold in a day is Rs. 5,900.
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Directions: The problem below consists of a question and two statements labelled (A) and (B) given below it. Read them carefully and decide which of the given statements is/are sufficient to answer the question. Choose the correct option accordingly. What is the ratio of Rohan's salary to Tim's salary? (A) If Rohan's pay was cut by 10% and Tim's pay was raised by 20%, they would earn the same amount. (B) Rohan earns Rs. 5000 more per month than Tim does.

  1. Statement (A) alone is sufficient, but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient, but statement (A) alone is not sufficient.

  3. Both statements (A) and (B) together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (A) and (B) together are not sufficient and additional data is needed.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement (A) provides the ratio: 0.9R = 1.2T, so R/T = 1.2/0.9 = 4/3. Statement (B) only provides a difference, which is insufficient for a ratio without knowing the base values.

Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare them and find the correct relationship between them. Quantity I: 'x'; Sammy was planning to get her room furnished whose length, breadth and height are in the ratio 5 : 3 : 6, respectively. The cost of furnishing all the sides, except the roof whose area is 150 sq. m, is 'x', if the rate of furnishing is Rs. 5 per m2 . Quantity II: Rs. 5500

  1. Quantity I > Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I = Quantity II or No relation

  5. Quantity I ≥ Quantity II
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

An amount of money was lent by Abhishek on simple interest at x% which gets increased by 2 times after 10 years. If y amount of money is invested in ratio 3 : 2, and the larger amount of money is invested at x + 5% and the smaller amount of money is invested at r% compounded annually, then the difference between their compound interests for 2 years will be Rs. 4000. Which of the following values of r are possible to obtain the value of y more than 12,000 but less than 14,000? (i) 2% (ii) 5% (iii) 10% (iv) 12% (v) 15%

  1. Only (i) and (ii)

  2. Only (iii) and (iv)

  3. Only (iv) and (iv)

  4. Only (ii), (iii) and (iv)

  5. None of these is possible.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: In this problem, a question is followed by statements marked (I), (II) and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. Salaries of A, B and C are in ratio of 5 : 6 : 8. A saves 25% of his salary and B saves 20% of his salary. Who among them saves the most money? I. 15% of C's salary is Rs. 800 more than 20% of A's salary. II. C saves Rs. 300 more than B does. III. A spends Rs. 1000 more than C does on electricity.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statements II and III

  4. All of the statements together

  5. None of the statements
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Salaries: 5x, 6x, 8x. Savings: A=0.25(5x)=1.25x, B=0.2(6x)=1.2x, C=0.8x (if we knew C's savings rate). I and II together allow calculation of x and comparison of savings. III is redundant.

Multiple choice

Directions: In this problem, a question is followed by statements marked (I), (II) and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. Ajay bought 4 chairs and a table. How much money did he pay? I. Cost of 4 chairs was Rs. 200 more than the cost of a table. II. Costs of a chair and a table were in the ratio of 3 : 8. III. Cost of two chairs was Rs. 100 less than the cost of a table.

  1. All three statements

  2. Any two statements

  3. Only statements I and II

  4. Only statements II and III

  5. Only statements I and III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C be chair cost and T be table cost. We have 4C + T = Total. I: 4C = T + 200. II: C/T = 3/8. III: 2C = T - 100. Any two of these equations allow solving for C and T, thus finding the total cost.

Multiple choice

Directions: In the following problem, a question is followed by three statements numbered (I), (II), and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. What is the salary of Ravi if the ratio of salaries of Ajay and Ravi is 5 : 8? I. Ajay's salary is Rs. 5000 less than Amar's salary. II. Ravi's salary is Rs. 10,000 more than Amar's salary. III. Ajay's salary is Rs. 15,000 less than Ravi's salary.

  1. Only statement II and either statement I or statement III

  2. Only statements I and II

  3. Only statement III

  4. Only statement III or statements I and II

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

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. What is the income of Gauri? I. The income of Ramesh is 80% of that of Gauri. Gauri earns Rs. 1500 more than Ramesh. II. The respective ratio of the incomes of Ramesh and Gauri is 25 : 22 and the difference between their incomes is Rs. 1500.

  1. The question can be answered by using statement I alone, but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone, but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using either of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: R = 0.8G, G = R + 1500. Substituting: G = 0.8G + 1500, 0.2G = 1500, G = 7500. Sufficient. Statement II: R/G = 25/22, G - R = 1500. This is a system of linear equations. Sufficient.

Multiple choice

Passage

Directions: In this problem, a question is followed by three statements, labelled as (A), (B) and (C). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question.

Find the monthly incomes of XYZ and PQR. (A) XYZ saves Rs. 2500 per month and PQR saves Rs. 5000 per month. (B) The monthly incomes of XYZ and PQR are in the ratio of 4 : 5. (C) The ratio of the expenses of XYZ and PQR is 5 : 6.

  1. Only A and B together are sufficient.

  2. All of them together are necessary.

  3. All of them together are not sufficient.

  4. Any one of A, B and C is sufficient.

  5. Any two of A, B and C are sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let incomes be 4x and 5x, and expenses be 5y and 6y. Savings are Income - Expense. So, 4x - 5y = 2500 and 5x - 6y = 5000. We have two equations with two variables (x, y), which is sufficient to find x and y. Statement A gives savings, B gives income ratio, C gives expense ratio. We need all three to form the system of equations.

Multiple choice

Passage

Directions: A table is given below for 5 employees of an organisation. Study the data carefully and answer the following question based on it. Employee Basic Pay (in Rs.) Perquisites (in Rs.) Deduction (in Rs.) Net Salary (in Rs.) A 21,800 28,600 - - B - - 4350 25,850 C 10,400 12,400 2800 20,000 D 11,200 13,800 - - E - 21,600 5700 - Additional Information *Net Salary = Basic Pay + Perquisites - Deduction *Deduction = Gratuity Fund (10% of Basic Pay) + Other Deductions

What would be D's deduction if the ratio of other deductions to the gratuity fund is 13 : 7?

  1. Rs. 1860

  2. Rs. 2080

  3. Rs. 2100

  4. Rs. 2120

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

Passage

Directions : In the following problem, you have to find out which of the given statements is/are redundant for determining the answer of the question asked or can be dispensed with.

What is the amount invested in Scheme Y? Statements: I. The amounts invested in Schemes X and Y are in the ratio 2 : 3. II. The amount invested in Scheme X is 40% of the total amount invested. III. The amount invested in Scheme X is Rs. 55,000.

  1. I and II

  2. I and III

  3. II and III

  4. Either I or II

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

To find the amount in Scheme Y, we need the total amount and the ratio. Statement I gives the ratio X:Y = 2:3. Statement II says X is 40% of the total, which implies Y is 60% of the total. Statement III gives the absolute value for X. We can find Y using (I and III) or (II and III). Thus, either I or II is redundant.

Multiple choice

Passage

Directions: The table given below shows the cost price (in rupees) of products in a particular shop and the mark-up% of different products. Products Cost Price (in Rs.) Mark-up% A - 26% B 5100 - C 4500 - D - 25% E - - F - 21% Notes: Some values are missing, you have to calculate them according to the question. Mark-up percentages are integral values.

Cost of product 'C' was 20% more than the cost of product 'D'. Find the approximate mark-up price of product 'F' if the ratio of cost prices of products 'D' and 'F' was 17 : 21.

  1. Rs. 6590

  2. Rs. 6353

  3. Rs. 5550

  4. Rs. 4580

  5. Rs. 5600
Reveal answer Fill a bubble to check yourself
B Correct answer