Ratio and Proportion Problems and Solutions

• 8. If Rs. 782 is divided into three parts, proportional to
  \begin{aligned}
  \frac{1}{2}:\frac{2}{3}:\frac{3}{4}
  \end{aligned}
  
  find the first part.

  1. 190
  2. 204
  3. 220
  4. 230

  Answer :

  Option B

  Explanation:

  \begin{aligned}
  \frac{1}{2}:\frac{2}{3}:\frac{3}{4} \\
  = 6:8:9\\
  \text{First part =} 782 * \frac{6}{23} \\
  = 204
  \end{aligned}

• 9. 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 :

  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}

• 10. 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 :

  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}

• 11. In a mixture 60 litres, the ratio of milk and water 2 : 1. If the this ratio is to be 1 : 2, then the quanity of water to be further added is

  1. 20 liters
  2. 30 liters
  3. 50 liters
  4. 60 liters

  Answer :

  Option D

  Explanation:

  Quantity of Milk = 60*(2/3) = 40 liters
  Quantity of water = 60-40 = 20 liters
  
  As per question we need to add water to get quantity 2:1
  
  => 40/(20+x) = 1/2
  => 20 + x = 80
  => x = 60 liters

• 12. 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 :

  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}

• 13. 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 :

  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}

• 14. 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 :

  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