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Ratio and Proportion Questions Answers

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

    1. 3
    2. 4
    3. 5
    4. 6
    Answer And Explanation

    Answer: Option 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

  • 16. 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 is

    1. 10
    2. 17
    3. 25
    4. 30
    Answer And Explanation

    Answer: Option 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}

  • 17. 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 salary.

    1. 32000
    2. 34000
    3. 38000
    4. 40000
    Answer And Explanation

    Answer: Option 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}

  • 18. A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have.

    1. Rs 484
    2. Rs. 480
    3. Rs 478
    4. Rs 470
    Answer And Explanation

    Answer: Option A

    Explanation:

    In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this.

    \begin{aligned}
    \frac{4}{15}A = \frac{2}{5}B \\
    A = \left(\frac{2}{5}*\frac{14}{4}\right)B \\
    A = \frac{3}{2}B \\
    \frac{A}{B} = \frac{3}{2} \\
    A:B = 3:2 \\
    \text{B's Share = }\frac{2}{5}*1210 = 484
    \end{aligned}

  • 19. If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number.

    1. 2:5
    2. 2:7
    3. 5:7
    4. 5:3
    Answer And Explanation

    Answer: Option D

    Explanation:

    Let the first number is A and second number is B.

    As per question

    \begin{aligned}
    \frac{40}{100}A = \frac{2}{3}B \\

    \frac{A}{B} = \frac{2}{3}*\frac{100}{40} \\
    \frac{A}{B} = \frac{5}{3} \\
    => A:B = 5:3

    \end{aligned}

  • 20. There are two numbers and their ratio is 3 : 9. If we substract 9 from both numbers then their ratio becomes 12 : 13, what is value is smaller number ?

    1. 23
    2. 27
    3. 31
    4. 33
    Answer And Explanation

    Answer: Option D

    Explanation:

    From question, lets assume that two numbers are 3x and 5x.

    \begin{aligned}
    \text{then, }\frac{3x - 9}{ 5x - 9} = \frac{12}{23}\\
    => \text{23(3x - 9) = 12(5x - 9)}\\
    => 9x = 99 \\
    => x = 11
    \end{aligned}
    So numbers are 3(11) = 33, 5(11) = 55.
    Smaller number is 33.