## 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