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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}

  • 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

  • 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}

  • 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}

  • 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

  • 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}

  • 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}