This page talks about Ratios and Proportions and give examples on solved problems of Ratios and Proportions.
RATIOS AND PROPORTIONS:
Ratio:
Comparison of two quantities is called ratio. “ : ” is the symbol for ratio. If p and q are two numbers, then ratio of p and q is p to q = p: q.
p:q = p/q
Here p is called Antecedent and q is called consequent.
For example, there are 7 apples and 5 oranges in a basket, the ratio of apples and oranges is 7/5 = 7:5
If there are 2 pens, 3 pencils, 1 eraser in a bag, then ratio of pencils to erasers is 3/1 = 3:1
Here 3:1 is not equal to 1:3.Order is important in ratios. In above example, ratio of pencils to erasers, so write pencils first and then eraser. Then ratio is 3:1.
Examples of Ratios and Proportions
Below are the Examples on Ratios and Proportions :
1) Ratio of 9 and 8 is 9/8 = 9:8
2) Ratio of 17 and 236 is 17/236 = 17:236
Proportion:
Expressing two ratios equal is called proportion.
If p: q and m: n are equal, then
p: q = m:n
Where p, q, m, n are in proportion
p and n are called extremes
q and m are called means
PRODUCT OF EXTREMES = PRODUCT OF MEANS
p x n = q x m
If three are known in a proportion, then we can find the fourth one.
Note:
p:q = m:n is nothing but p/q = m/n
Mean Proportional:
A number x such that x/c = d/x where c, d are two numbers , then x is called mean proportional of c and d
x/c = d/x
x2 = cd
x = + ?cd, -?cd
Examples:
1) 4 is the mean proportional of 2 and 8
Here x = 4, c =2, d = 8
x2 = cd
4x4 = 2x8
16 = 16
2) 6 is the mean proportional of 9 and 4
Here x =6, c =9, d = 4
x2 = cd
6x6 = 9x4
36 = 36
Solved Problems of Ratios and Proportions
Following are solved problems on ratios and propotions :
1) Write the simplest form for this ratio 25:15.
Solution:
25:15 = 25/15 5 is common multiple of 25 and 15
= 5/3
2) In a school, there are 14 boys, 16 girls. Find the ratio of girls to total number
of students?
Solution:
Number of girls = 16
Number of boys = 14
Total number = Number of boys + number of girls
= 14 + 16
= 30
Ratio = number of girls / total number
= 16/30
= 8/15
= 8:15
3) In a cupboard, the ratio of green balls to yellow balls is 7 to 8. How many of
900 balls are yellow?
Solution:
Ratio of green balls to yellow balls = 7/8
Ratio of yellow balls to total balls = 8/ 7+8
= 8/15
Number of yellow balls = (ratio of yellow balls to total balls) x total number of balls
= 8/15 x 900
= 8 x 900 /15
= 7200/15
= 480
4) Solve y/7 = 10/14
Solution:
y/7 = 10/14 multiply both sides by 7
7(y/7)= 7(10/14)
y = 70/14
y = 5
Check:
5:7 = 10:14
Product of extremes = product of means
5 x 14 = 7 x 10
70 = 70
5) Solve 3/k = 9/6
Solution:
3:k = 9:6
product of extremes = product of means
3 x 6 = k x 9
18 = 9k divide both sides by 9
18/9 = 9k/9
2 = k
k = 2
6) Solve (y - 3)/4 = (y + 1)/5
Solution:
(y-3) : 4 = (y+1) : 5
product of extremes = product of means
(y-3) x 5 = 4 x (y+1)
5(y-3) = 4(y+1)
5 x y - 5 x 3 = 4 x y + 4 x 1
5y - 15 = 4y + 4 add 15 to both sides
15 15
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5y = 4y + 19 subtract 4y from both sides
-4y -4y
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y = 19