This document provides examples and explanations of ratios and continued ratios. It begins by defining a ratio as a comparison of two numbers using a colon or fraction. Examples are given comparing numbers of marbles, books, and oranges. Conversions between grams, kilograms, meters, and centimeters are also shown. The document then explains that a continued ratio can be used to compare more than two quantities by writing out the individual ratios and multiplying the middle terms appropriately. Several examples are worked out finding the continued ratio a:b:c given the individual ratios a:b and b:c. Practice problems are also provided for the reader to work through.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
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2. Ratio:
A ratio is a comparison of two numbers.
We generally separate the two numbers in the ratio
with a colon(:),
suppose we want to write the ratio 4 and 8
we can write this as 4:8 or as a fraction 4/8 and
we say the ratio is four to eight.

3. Example-1:
Humza has a bag with 4 marbles, 7 books and 2 oranges.
• What is the ratio of books to marbles.
7:4 or 7/4
• What is the ratio of oranges to books.
2:7 or 2/7

4. Example-2:
Find the ratio of 50 grams to 2kilograms.
50grams : 2 kg (1 kg = 1000 grams)
=50g : 2000g
= 1: 40

5. Memories the following
1 Kilogram = 1000 grams
1 Meter = 100 cm
1 Feet = 12 inches
1 Hour = 60 minutes
1 Rupee = 100 paisas

6. DO YOURSELF
1. Find the ratio of 3 hours to 50 minutes.
2. Find the ratio of 30 minutes to 01 hour.
3. Find the ratio of 400 cm to 3 meters.
4. Find the ratio of 100 grams to 01 kilogram.
5. Find the ratio of Rs.10 to Rs.100.
6. Find the ratio of 60 paisa to 02 rupees.
7. Find the ratio of 40 inches to 5 feet.
8. Find the ratio of 30 minutes to 2 hours and 30 minutes.
Answers
1. 18:5 2. 1:2 3. 4:3 4. 1:10
5. 1:10 6. 3:10 7. 2:3 8. 1:5

7. Continued ratio (Combined ratio)
When more than two quantities are to be compared,
we have to use concept of continued ratio.
Example-3:
If a : b = 3 : 5 and b : c = 5 : 7, find a:b:c.
Solution:
a : b : c
3 : 5
5 : 7
3 : 5 : 7 (since middle term is same)
Hence a : b : c = 3: 5 : 7

8. Example-4:
If a : b = 2 : 5 and b : c = 4 : 3, find a:b:c.
Solution:
a : b : c
2 : 5
4 : 3
8 : 20 : 15 (if middle term is not same then
multiply 2 with 4, 4 with 5
and 3 with 5)
Hence a : b : c = 8 : 20 : 15

9. Example-5:
If a : b = 3 : 2 and a : c = 4 : 7, find a:b:c.
Solution:
since a is common then we can write a:b:c
like this
b : a : c
2 : 3
4 : 7
8 : 12 : 21 (since middle term is not same)
Hence a : b : c = 12: 8 : 21

10. DO YOURSELF
Find the ratio a:b:c when
a) a:b = 1:4 and b:c = 4:7 c) a:b = 2:5 and a:c = 2:7
b) a:b = 3:7 and b:c = 6:15 d) a:b = 5:7 and a:c =3:4
Answers
(a) 1:4:7
(b) 18:42:105
(c) 2:5:7
(d) 15:21:20