Ratio and Proportion Problems and Solutions

• 1. Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's. What is B's share

  1. Rs 10
  2. Rs 20
  3. Rs 24
  4. Rs 28

  Answer :

  Option B

  Explanation:

  Let C = x. Then A = (x—20) and B = (x—40).
  x + x - 20 + x - 40 = 120 Or x=60.
  A:B:C = 40:20:60 = 2:1 :3.
  B's share = Rs. 120*(1/6) = Rs. 20

• 2. 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 :

  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}
  

• 3. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

  1. 2:5
  2. 3:5
  3. 4:5
  4. 6:5

  Answer :

  Option C

  Explanation:

  Let the third number be x.
  First Number (120/100)*x = 6x/5
  Second Number (150/100)*x = 3x/2
  
  Ratio = 6x/5:3x/2
  => 4:5
  

• 4. 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. 83.5%
  2. 87.5%
  3. 88.5%
  4. 89.5%
  5. Rs 484
  6. Rs. 480
  7. Rs 478
  8. Rs 470

  Answer :

  Option E

  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}

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

  1. 2
  2. 3
  3. 4
  4. 6
  5. 39000
  6. 40000
  7. 43000
  8. 49000

  Answer :

  Option E

  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. A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is

  1. 4:5
  2. 9:5
  3. 8:5
  4. 9:2

  Answer :

  Option B

  Explanation:

  Dog : Hare = (3*3) leaps of hare : 5 leaps of hare
  = 9 : 5

• 7. In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of students in the college is

  1. 420
  2. 520
  3. 620
  4. 720

  Answer :

  Option B

  Explanation:

  Let the boy are 8x and Girls are 5x
  
  => 5x = 200
  => x = 40
  
  Total students = 8x+5x = 13x = 13(40) = 520