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

In an express train the number of passengers travelling in AC sleeper class, first class, and sleeper class are in the ratio 1 : 2 : 3 and the fares of each classes are in the ratio 5 : 4 : 2. If the total income from this train is Rs. 54000, then what is the income from AC sleeper class ?

  1. Rs. 11210 (approx)

  2. Rs. 13210 (approx)

  3. Rs. 14210 (approx)

  4. Rs. 16210 (approx)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Income = Passengers * Fare. Ratios: Passengers (1:2:3), Fares (5:4:2). Income ratio = (1*5):(2*4):(3*2) = 5:8:6. Total parts = 19. Income from AC sleeper = (5/19) * 54000 = 14210.52.

Multiple choice

The ratio of the incomes of $\mathrm { A }$ and $\mathrm { B }$ is $5 : 4$ andthe ratio of their expenditures is $3 : 2 .$ If at the end of the year, each saves $\mathrm { Rs } .1600$ , then the income of $\mathrm { A }$ is :
  1. $Rs. 3400$
  2. $Rs. 3600$
  3. $Rs. 4000$
  4. $Rs. 4400$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 5x and 4x, and expenditures be 3y and 2y. Savings are 5x - 3y = 1600 and 4x - 2y = 1600. Solving this system gives x = 800, so A's income is 5 * 800 = 4000.

Multiple choice

Two statements numbered I and II given below. Decide whether the data provided in the statements is sufficient to answer the question. Total money with Naresh and Ajay is $28$ % of that with Usman. How much money is Ajay having? I. Usman has got Rs $75000$ II. The ratio of money of Naresh to money held by Ajay is $1 : 3$

  1. The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question

  2. The data in statement II alone are sufficient to answer the question, while the data in statement i alone are not sufficient to answer the question

  3. The data either in statement I alone or in statement II alone are sufficient of answer the question

  4. The data given in both statements I and II together are necessary to answer the question

  5. The data given in both statements I and II together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let N, A, U be the money of Naresh, Ajay, and Usman. We know N+A = 0.28U. We want to find A. Statement I gives U=75000, so N+A = 21000. Statement II gives N/A = 1/3, so N = A/3. Substituting gives A/3 + A = 21000, which allows solving for A. Both statements are required.

Multiple choice

$P,Q$ have position vectors $\overrightarrow { a } $ and $\overrightarrow { b }$ relative to the origin $O$ and $X,Y$ divide $\overrightarrow { OQ }$ internally and externally respectively in the ratio $2:1$. Vector $\overrightarrow { XY }=$
  1. $\displaystyle \dfrac { 3 }{ 2 } \left( \overrightarrow { b } -\overrightarrow { a }  \right) $
  2. $\displaystyle \dfrac { 3 }{ 4 } \left( \overrightarrow { b } -\overrightarrow { a }  \right) $
  3. $\displaystyle \dfrac { 5 }{ 6 } \left( \overrightarrow { b } -\overrightarrow { a }  \right) $
  4. $\displaystyle \dfrac { 4 }{ 3 } \left( \overrightarrow { b } -\overrightarrow { a }  \right) $
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

The monthly incomes of Davinder and Malkit are in the ratio 4 : 5 and their expenses are in the ratio 5 : 6. If Davinder saves Rs. 25 per month and Malkit saves Rs. 50 per month, what are their respective incomes?

  1. Rs. 720 and Rs. 900

  2. Rs. 400 and Rs. 500

  3. Rs. 160 and Rs. 200

  4. Rs. 800 and Rs. 1000

  5. Rs. 400 and Rs. 550
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let incomes be 4x and 5x. Expenses are 5y and 6y. 4x - 5y = 25 and 5x - 6y = 50. Solving this system: multiply first by 6, second by 5: 24x - 30y = 150 and 25x - 30y = 250. Subtracting gives x = 100. Incomes are 400 and 500.

Multiple choice

In an investment of Rs. 1,00,000, Ram and Sunder earn a profit of Rs. 30,000. If they share the profit in the ratio 1 : 2, then find the profit of Ram and the profit of Sunder, respectively.

  1. Rs. 20,000 and Rs. 10,000

  2. Rs. 10,000 and Rs. 20,000

  3. Rs. 18,000 and Rs. 12,000

  4. Rs. 15,000 and Rs. 15,000

  5. Rs. 12,000 and Rs. 18,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total profit is 30,000, shared in a 1:2 ratio. The sum of the ratio parts is 1 + 2 = 3. Ram's share is (1/3) * 30,000 = 10,000, and Sunder's share is (2/3) * 30,000 = 20,000.

Multiple choice

The ratio of incomes of two persons is 5 : 3 and that of then expenditure is 9 : 5. Find the income of each person if they save Rs. 1300 and Rs. 900 respectively.

  1. Rs. 4000, Rs. 2400

  2. Rs. 3000, Rs 1800

  3. Rs. 5000, Rs. 3000

  4. Rs. 4500, Rs. 2900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Income ratio 5:3, expenditure 9:5, savings 1300 and 900. (5x - 1300) / (3x - 900) = 9/5. 25x - 6500 = 27x - 8100 => 2x = 1600 => x = 800. Incomes are 5*800=4000 and 3*800=2400.

Multiple choice

The ratio of incomes of Alexander and Ibrahim is 5 : 3 and that of their expenditures is 9 : 5. If they save Rs. 5200 and Rs. 3600, then their incomes are

  1. Rs. 16000 and Rs. 9600

  2. Rs. 12000 and Rs. 7200

  3. Rs. 20000 and Rs. 12000

  4. Rs. 18000 and Rs. 10800

  5. Rs. 22000 and Rs. 14000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let incomes be 5x and 3x, expenditures 9y and 5y. 5x - 9y = 5200 and 3x - 5y = 3600. Solving this system: multiply first by 3 and second by 5: 15x - 27y = 15600 and 15x - 25y = 18000. Subtracting gives 2y = 2400, so y = 1200. Then 3x - 6000 = 3600, 3x = 9600, x = 3200. Incomes are 5(3200)=16000 and 3(3200)=9600.

Multiple choice

The total profit earned by Raman and Stella is Rs. 1,20,000, which they share in the ratio 1 : 5. How much more money should be given to Raman so that the profit is distributed equally?

  1. Rs. 35,000

  2. Rs. 40,000

  3. Rs. 45,000

  4. Rs. 50,000

  5. Rs. 55,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total profit is 1,20,000. Ratio 1:5 means Raman gets 20,000 and Stella gets 1,00,000. For equal distribution, each should get 60,000. Raman needs 60,000 - 20,000 = 40,000 more.