Ratio and Proportion Questions Answers

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

  1. 8:12:9
  2. 2:3:8
  3. 2:3:9
  4. 2:3:12

  Answer And Explanation

  Answer: Option 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}

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• 2. Find the fourth proportion to 2,3,6

  1. 18
  2. 12
  3. 9
  4. 4

  Answer And Explanation

  Answer: Option C

  Explanation:

  2:3 :: 6:x
  
  => 2/3 = 6/x
  => x = 18/2
  => x = 9

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• 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

  Answer And Explanation

  Answer: Option 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}
  

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

  1. 15:24:30:35
  2. 16:24:30:35
  3. 17:24:30:35
  4. 18:24:30:35

  Answer And Explanation

  Answer: Option 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}

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

  1. 2
  2. 3
  3. 4
  4. 6

  Answer And Explanation

  Answer: Option 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
  

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

  1. 14:5
  2. 15:5
  3. 16:5
  4. 17:5

  Answer And Explanation

  Answer: Option 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}

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• 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 salaries.

  1. 20:33:60
  2. 21:33:60
  3. 22:33:60
  4. 23:33:60

  Answer And Explanation

  Answer: Option 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}

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