This document discusses compound proportions, which involve relating two or more quantities. It provides four rules for solving compound proportions based on whether the quantities are directly or inversely related. It then gives eight examples showing how to set up and solve compound proportion word problems involving rates like production, wages, distance, and time. The examples calculate unknown values like number of items, amount of wages, distance or time taken by relating the given and unknown quantities using the appropriate rule for direct or inverse relationships.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
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2. Compound Proportion
The proportion involving two or more quantities is called compound proportion.
The quantities could be directly related or inversely related or both.
Rules for computation:
quantity1 quantity2 quantity3
a b c
d e x
If quantity1 and quantity2 are directly related and quantity2 and quantity3 are also
directly related then
a b d e
c x
 

Case-I

3. Case-2
If quantity1 and quantity2 are directly related and quantity2 and quantity3 are
inversely related, then
b c e x
a d
 

Case-3
If quantity1 and quantity2 are inversely related and quantity2 and quantity3 are
directly related, then
a b d e
c x
 

Case-4
If quantity1 and quantity2 are inversely related and quantity2 and quantity3 are
also inversely related, then
a × b × c = d × e × x

4. Example-1
A factory can manufacture 200 items in a day using 10 machines. How many items
can be manufactured using 14 machines in 04 days?
Solution:
items machines days
200 10 1
x 14 4
x 14 4
200 10 1
56
x 200
10
 
 
x = 1120 items

5. Example-2
If 08 men earn Rs.9600in 05 days. How much will 09 men earn in 07 days?
Solution:
amount days men
9600 5 8
x 7 9
x 7 9
9600 5 8
7 9
x Rs.15120
5 8
 
    

6. Example-3
30 machines produce 1000 screws in 100 hours. How many screws can 24
machines produce in 60 hours?
Solution:
No. of screws machines hours
1000 30 100
x 24 60
x 24 60
1000 30 100
24 60
x 480screws
30 100
 
   

7. Example-4
If 09 men are paid Rs.15120 for 07 days work, what will be the wages of 08 men
for 05 days?
Solution:
wages men days
15120 9 7
x 8 5
𝑥
15120
=
8
9
×
5
7
𝑥 =
8
9
×
5
7
× 15120
𝑥 = 𝑅𝑠. 9600

8. x 10 45
5 15 75
 
x 450
5 1125
450
x 5
1125

 
Example-5
10 men can lay a road 75 km long in 05 days. In how many days can 15 men lay
a road of 45 km long.
Solution:
Days Men Km
5 10 75
x 15 45
x = 2 days

9. Example-6
20 men can build a road 15 k.m long in 18 days.How long will 25 men take to
complete a 10 k.m long road?
Solution:
days men km
18 20 15
x 25 10
x 20 10
18 25 15
20 10
x 9.6days
25 15
 
   

10. Example-7
05 photocopiers can produce 90,000 copies in 06 hours a day. How many
photocopiers will be required to produce 168000 copies working 08 hours a day?
Solution:
photocopiers photocopies hours
5 90000 6
x 168000 8
x
5
=
168000
90000
×
6
8
x =
168000
90000
×
6
8
× 5
x = 7 photocopiers

11. Example-8
25 labourers can construct 15 rooms in 18 days. In how many days can 10
labourers complete 10 rooms of the same size?
Solution:
days labourers rooms
18 25 15
x 10 10
x 25 10
18 10 15
25 10
x 30days
10 15
 
   