Ratio and Proportion Problems and Solutions

• 15. 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
  5. Adopt a more practical ideology of structural adjustment.
  6. Change its ideology to one encouraging both public and private sector investment in basic infrastructure.
  7. Reduce the influence of the US and Britain in its functioning.
  8. Support China’s involvement in developing Africa.

  Answer :

  Option F

  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}

• 16. 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 :

  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}

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

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

  Answer :

  Option C

  Explanation:

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

• 18. 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 :

  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}

• 19. If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

  1. 10
  2. 14
  3. 18
  4. 22

  Answer :

  Option B

  Explanation:

  Let the numbers be 3x, 2x and 5x.
  Then,
  9x + 4x + 25x =1862
  ⇒ 38x = 1862
  ⇒ x = 49 ⇒ x = 7.
  middle number = 2x = 14