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Ratio and Proportion Questions Answers

Ratio and Proportion Questions Answers (MCQ) listings with explanations includes questions on Ratios, Proportions, Third and Fourth proportion questions and other important questions which are useful in various competitive exams.

1) If a:b = 2:3 and b:c = 4:3, then find a:b

  • 1) 8:12:9
  • 2) 2:3:8
  • 3) 2:3:9
  • 4) 2:3:12
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Ans.   A
Explanation :
\begin{aligned} a:b = 2:3 \b:c = 4:3 = (4*\frac{3}{4} : 3*\frac{3}{4}) \= 3:\frac{9}{4} \a:b:c = 2:3:\frac{9}{4} \= 8:12:9 \end{aligned}

2) Find the fourth proportion to 2,3

  • 1) 18
  • 2) 12
  • 3) 9
  • 4) 4
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Ans.   C
Explanation :
2:3 :: 6:x => 2/3 = 6/x => x = 18/2 => x = 9

3) If A:B:C = 2:3:4, then find \begin{aligned} \frac{A}{B}:\frac{B}{C}:\frac{C}{A} \end{aligned}

  • 1) 5:9:24
  • 2) 6:9:24
  • 3) 7:9:24
  • 4) 8:9:24
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Ans.   D
Explanation :
Let A = 2x, B = 3x, C = 4x, then, \begin{aligned} \frac{A}{B} = \frac{2x}{3x} = \frac{2}{3} \\frac{B}{C} = \frac{3x}{4x} = \frac{3}{4} \\frac{C}{A} = \frac{4x}{2x} = \frac{2}{1} \ => \frac{A}{B}:\frac{B}{C}:\frac{C}{A} \= \frac{2}{3}:\frac{3}{4}:\frac{2}{1} \= 8:9:24 \end{aligned}

4) If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C

  • 1) 15:24:30:35
  • 2) 16:24:30:35
  • 3) 17:24:30:35
  • 4) 18:24:30:35
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Ans.   B
Explanation :
\begin{aligned} A:B = 2:3 \B:C = 4:5 = (4*\frac{3}{4} : 5*\frac{3}{4}) \= 3:\frac{15}{4} \C:D = 6:7 = (6*\frac{15}{24} : 7*\frac{15}{24}) \= \frac{15}{4}:\frac{35}{8} \A:B:C:D = 2:3:\frac{15}{4}:\frac{35}{8} \ = 16:24:30:35 = 8:12:9 \end{aligned}

5) If 2 : 9 :: x : 18, then find the value of

  • 1) 2
  • 2) 3
  • 3) 4
  • 4) 6
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Ans.   C
Explanation :
Treat 2:9 as 2/9 and x:18 as x/18, treat :: as = So we get 2/9 = x/18 => 9x = 36 => x = 4

6) if x:y = 1:3, then find the value of (7x+3y):(2x+

  • 1) 14:5
  • 2) 15:5
  • 3) 16:5
  • 4) 17:5
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Ans.   C
Explanation :
let x = 1k and y = 3k, so \begin{aligned} = \frac{7(k)+3(3k)}{2(k)+1(3k)} \= \frac{16k}{5k} \= 16:5 \end{aligned}

7) The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salarie

  • 1) 20:33:60
  • 2) 21:33:60
  • 3) 22:33:60
  • 4) 23:33:60
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Ans.   D
Explanation :
Let A salary be 2k B salary be 3k and C salary be 5k \begin{aligned} \text{A's new salary = }\frac{115}{100}*2k \ = \frac{23}{10}k \\text{B's new salary = }\frac{110}{100}*3k \ = \frac{33}{10}k \\text{C's new salary = }\frac{120}{100}*5k \ = 6k \ \text{New ratio = }\\frac{23k}{10}:\frac{33k}{10}:6k \ = 23:33:60 \\end{aligned}

8) The least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21,

  • 1) 3
  • 2) 4
  • 3) 5
  • 4) 6
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Ans.   A
Explanation :
Let x is subtracted. Then, \begin{aligned} \frac{(6-x)}{(7-x)}< \frac{16}{21} \ 21(6—x) < 16(7—x)\=> 5x > 14 = x > 2.8 \end{aligned} Least such number is 3

9) The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number

  • 1) 10
  • 2) 17
  • 3) 25
  • 4) 30
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Ans.   D
Explanation :
\begin{aligned} a:b = 2:3 \\ b:c = 5:8 = (5*\frac{3}{5} : 8*\frac{3}{5}) \\ = 3:\frac{24}{5} \\ a:b:c = 2:3:\frac{24}{5} \\ = 10:15:24 \b = 98*\frac{15}{49} \= 30 \end{aligned}

10) Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs 4000, the new ratio becomes 40:57. What is Sumit present sala

  • 1) 32000
  • 2) 34000
  • 3) 38000
  • 4) 40000
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Ans.   C
Explanation :
Let the original Salaries of Ravi and Sumit is 2x and 3x. So as per question \begin{aligned} \frac{2x+4000}{3x+4000} = \frac{40}{57} \=> 57(2x+4000) = 40(3x+4000) \=> 6x = 68000 \=> 3x = 34000 \ \text{ Sumit Salary =} 3x+4000 \34000 + 4000 = 38000 \end{aligned}
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