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

The employer reduces the number of employees in the ratio 9 : 8 and increases their wages in the ratio 14 : 15 If the previous wage bill was Rs 189000 what is the amount by which the new wage bill will increase or decrease?

  1. Rs 21000

  2. Rs 10000

  3. Rs 9000

  4. Rs 25000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial employees = 9x, wages = 14y. Initial bill = 126xy = 189000. xy = 1500. New employees = 8x, wages = 15y. New bill = 120xy = 120 * 1500 = 180000. Decrease = 189000 - 180000 = 9000.

Multiple choice

Ratio of the incomes of A, B and C last year was 3 : 4 : 5 The ratio of their individuals incomes of the last year and this year are 4 : 5, 2 : 3 and 3 : 4 respectively If the sum of their present incomes is Rs 78800 then find the present individual income of A, B and C

  1. Rs 10000, Rs 40000, Rs 28800

  2. RS 18000, Rs 28800, Rs 32000

  3. Rs 45000, Rs 12800, Rs 21000

  4. RS 20000, Rs 14600, Rs 44200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Last year incomes: A=3k, B=4k, C=5k. This year incomes: A=3k*(5/4)=3.75k, B=4k*(3/2)=6k, C=5k*(4/3)=6.66k. Sum = 3.75k + 6k + 6.66k = 16.416k = 78800. Solving for k gives k=4800. Present incomes: A=18000, B=28800, C=32000.

Multiple choice

The ratio of prices of onion last year and this year is $5 : 6$. The ratio of prices of potato last year and this year is $7 : 8$. The sum of prices of a kg of onion and potato this year is $48$ Rs. Find the price of onion (in Rs) last year if it was $\displaystyle \left ( \frac{20}{21} \right )$ of the price of potato last year?
  1. $15$
  2. $20$
  3. $25$
  4. $30$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Onion: Last year = 5x, This year = 6x. Potato: Last year = 7y, This year = 8y. 6x + 8y = 48. Onion last year (5x) = (20/21) * Potato last year (7y) = (20/21) * 7y = (20/3)y. So 5x = 20y/3, x = 4y/3. Substitute: 6(4y/3) + 8y = 48. 8y + 8y = 48. 16y = 48, y = 3. x = 4(3)/3 = 4. Onion last year = 5x = 5(4) = 20.

Multiple choice

The ratio of Rs. 4 and 80 paise is__

  1. 1 : 5

  2. 1 : 30

  3. 5 : 1

  4. 30 :1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Convert units to the same scale: 4 Rs = 400 paise. The ratio is 400 : 80, which simplifies to 5 : 1.

Multiple choice

Rs. 535 is divided among A, B and C so that if Rs. 15, Rs. 10. Rs. 30 be subtracted from their respective shares, the remainders may be in the ratio 4: 5 : 7, what was their initial shares (in Rs.) ?

  1. 135, 160, 240

  2. 160, 280, 318

  3. 150.210,325

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Subtracting the given amounts from the total (535 - 15 - 10 - 30 = 480) leaves 480 to be divided in ratio 4:5:7. The sum of parts is 16, so each part is 30. The remainders are 120, 150, and 210, and adding back the subtracted amounts gives 135, 160, and 240.

Multiple choice

The following question accompanied by three statements I, II and III. We have to determine which statements is/are sufficient to answer the question. What is the sum of two numbers? I. The bigger of these two numbers is $6$ more than the smaller number. II. $40\%$ of the smaller number is equal to $30\%$ of the bigger number. III. The ratio between half of the bigger number and one-third of the smaller number is $2:1.$

  1. Only II and II are sufficient

  2. Only I and II are sufficient

  3. I and either II or III is sufficient

  4. All, I, II, and III together are sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I gives the difference between the numbers. Statement II gives their ratio as 4:3, and statement III also gives the same ratio. Combining the difference with either ratio determines both numbers and their sum.