Ratio and Proportion Solution11





In this page ratio and proportion solution11 we are going to see solution of each question from the worksheet ratio and proportion.

(18) If p : q = 7 : 4 find (5 p – 3 q) : (7 p + 3 q)

Solution:

p : q = 7 : 4

p/q = 7/4

(5 p – 3 q) : (7 p + 3 q) = (5 p – 3 q)/(7 p + 3 q)

Divide both numerator and denominator by q, so we get 

                                       = (5(p/q) – 3)/(7(p/q) + 3)

                                       = (5(7/4) – 3)/(7(7/4) + 3)

                                       = [(35/4) – 3]/[(49/4) + 3)]

                                       = [(35 – 12)/4]/[(49 + 12)/4]

                                       = [23/4]/[61/4]

                                       = [23/4] x [4/61]

                                       = (23/61)

                                      = 23 : 61


(19) If (4 x + 5) : (3 x + 11) = 21 : 23,find x

Solution:

(4 x + 5) : (3 x + 11) = 21 : 23

(4 x + 5)/(3 x + 11) = 21/23

23 (4 x + 5) = 21 (3 x + 11)

92 x + 115 = 63 x + 231

92 x – 63 x = 231 – 115

29 x = 116

     x = 116/29

     x = 4


(20) If a : b = 5 : 3, find (2 a + 5 b) : (a + 3 b)

Solution:

a : b = 5 : 3

a/b = 5/3

(2 a + 5 b) : (a + 3 b) = (2 a + 5 b)/(a + 3 b)

Divide both numerator and denominator by b, so we get 

                              = [2 (a/b) + 5]/[(a/b) + 3]                                 

                              = [2 (5/3) + 5]/[(5/3) + 3]

                              = [(10/3) + 5]/[(5/3) + 3]

                              = [(10+ 15)/3]/[(5 + 9)/3]

                               = [25/3]/[14/3]

                               = [25/3] x [3/14]

                               = [25/14]

                               =  25 : 14


(21) Find a number which has the same ratio with 4/9 as 2/11 has with 7/33

Solution:

Let x be the required number

x : (4/9) = (2/11) : (7/33)

 x/(4/9) = (2/11)/(7/33)

 9 x/4 = (2/11) x (33/7)

 9 x/4 = (6/7)

   x = (6/7) x (4/9)

   x = 2/21

ratio and proportion solution11ratio and proportion solution11