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

- Back to worksheet
- Time and Work
- Time and Distance
- Ratio and Proportion
- Average
- Percentage
- Profit and Loss
- Hour Clock Arithmetic
- Day Arithmetic
- Month Arithmetic
- Equations
- Odd man out
- Problems on Ages
- Pipes and Cisterns
- Boats and Streams
- Mixture Problems
- Problems on Trains