Ratio and Proportion I


   
 
Illustrative Examples
Example 1:
 
Find the compounded ratio of
 
a) 5:14 and 7:15
 
b) a+b:a-b; (a2-b2):(a2+b2) and a2+b2:(a+b)2
 
Suggested answer:
 
a) The compounded ratio of 5:14 and 7:15 is
 
 
b)The compounded ratio of a+b:a-b; a2-b2:a2+b2 and a2+b2:(a+b)2 is (a+b) (a2-b2) (a2+b2) : (a-b) (a2+b2) (a+b)2
 
(a+b) (a+b) (a-b) : (a-b) (a+b) (a+b)
 
 
1:1
 
Example 2:
 
If x:y=3:4 find value of (4x+3y) : (2x+5y).
 
Suggested answer:
 
 
 
 
Example 3:
 
If 2x - y : 3x - 2y = 3:4, find x:y.
 
Suggested answer:
 
 
4(2x-y)=3(3x-2y)
 
8x-4y=9x-6y
 
 
6y-4y=9x-8x
 
2y=x
 
 
x:y=2:1
 
Example 4:
 
In the ratio 7:8, if the consequent is 40, what is the antecedent?
 
Suggested answer:
 
 
 
x=35
 
Antecedent=35.
 
Example 5:
 
If a:b = 5:8. Find the value of a2b+ab2:a3+b3.
 
Suggested answer:
 
 
 
 
 
 
 
 
 
Example 6:
 
Find
 
a) reciprocal ratio of 3:5
 
b) duplicate ratio of 2:3
 
c) triplicate ratio of 3:4
 
d) sub duplicate ratio of 25:16
 
e) sub triplicate ratio of 27:8
 
Suggested answer:
 
a) Reciprocal ratio of 3:5
 
 
b) Duplicate ratio of 2:3
 
=22:32=4:9
 
c) Triplicate ratio of 3:4
 
= 33:43
 
= 27:64
 
d) Sub duplicate ratio of 25:16
 
 
=5:4
 
e) Sub triplicate ratio of 27:8
 
 
= 3:2
 
Example 7:
 
If a:b=4:5, b:c=6:7, find a:c and a:b:c.
 
Suggested answer:
 
 
 
 
 
Hence a:c = 24:35
 
{a:b = 4:5} x 6
 
{b:c = 6:7} x 5
 
a:b = 24:30
 
b:c = 30:35 (To make b equal in both ratio)
 
Hence a:b:c = 24:30:35
 
Example 8:
 
 
Suggested answer:
 
 
 
12a+18 = 25a-190
 
25a-12a = 18+190
 
13a = 208
 
 
a = 16
 
Example 9:
 
Two numbers are in the ratio 3:4. If 8 is added to the numbers, the ratio becomes 5:6. Find the numbers.
 
Suggested answer:
 
 
 
6x+48 = 5y+40
 
 
 
 
y = 16
 
 
 
Example 10:
 
Divide Rs.256 in the ratio 7:9.
 
Suggested answer:
 
Let x be common to the ratio 7:9.
 
7x, 9x
 
7x+9x=256
 
16x=256
 
 
Hence, the parts are 7 x 16 = Rs.112
 
and 9 x 16 = Rs.144.
 
 
     
   
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