1. Ratio and Proportion
By
Vishwanath K

2. Some important tips
 First part = a1/(a1+a2) * A
 Second part = a2/(a1 + a2) * A
Problems:
1) Two numbers are in the ratio 8:9, If sum of the numbers is 119,find the numbers.
2) Dividing Rs 3,200 among P,Q,R in the ratio 5:2:9 , Find the amount received by Q.

3.  In ratios a:b and c:d
a:b > c:d if ad>bc i.e. a/b>c/d
a:b < c:d if ad<bc i.e. a/b<c/d
• Problem:
1) Compare 5:7 and 2:3

4.  If a/b = 1, then
(a+x)/(b+x)=a/b = 1 (a-x)/(b-x)=a/b = 1
 If a/b > 1, then
(a+x)/(b+x) < a/b (a-x)/(b-x) > a/b
 If a/b < 1, then
(a+x)/(b+x) > a/b (a-x)/(b-x) < a/b

5. • Problems :
• Consider the ratio 7/5 and explain the above
properties.
• Consider the ratio 4/9 and explain the above
properties

6. Proportion
a,b,c,d are in proportion if
Product of means = Product of extremes
Consider a:b = c:d
Means = b and c Extremes = a and d
The ratios are in proportion only if
ad = bc

7. When a:b = c:d or a/b = c/d
1) b/a = c/d
2) a/c = b/d
3) c/a = d/b
4) (a+b)/b = (c+d)/d
5) (a-b)/b = (c-d)/d
6) (a+b) / (a-b) = (c+d) / (c-d)
7) a/(a-b) = c/ (c-d)

8. Important tips
• In a : b = c : d
1st proportion 2nd proportion 3rd proportion 4th proportion
Third proportion:
If a,b,c are in continued proportion, then
a:b = b:c i.e. b² = ac

9. • Problems.
• Find the mean proportional between 9 and
16.
• If 3,x,27 are in continued proportion, Find x

10. Three terms
Given a:b = x:y and b:c = p:q
a : b = x : y
b : c = p : q
a : b : c = xp : py : yq
a:c = xp : yq
Problem: If incomes of Ram and Shyam are in the ratio 3:5 and that of Shyam and
Mohan are in the ratio of 7:4, find the ratios of incomes of Ram, Shyam and
Mohan.

11. Four terms
Given a:b = x:y, b:c = p:q, c:d = m:n
a : b = x : y
b : c = p : q
c : d = m : n
a:b:c:d = xpm : ypm : yqm : yqn
a : d = xpm : yqn
Problem: Find B’s share in Rs 6,300 if A:B = 2:3, B:C = 4:5 and C:D = 3:7.