1. Direct proportion word problems
In Tamil, substitute the word “variation” in existing variations PPTs with “proportion”

2. Proportion
When two ratios (a:b) and (c:d) are equal, we say that the ratios are in proportion.
It is denoted as a:b :: c:d
Read as ‘a is to b’ as ‘c is to d’
Refer existing variations PPT

3. Examples of Proportion in real life
What happens when
You buy
more pens ↑ ?
Costs you more ↑
Number of
students are
more ↑?
More number
of teachers ↑
Speed of the
car increases ↑?
Time taken to reach
destination
decreases ↓
Number of people
working increases ↑?
Time taken to
finish work
decreases ↓

4. Direct Proportion Answer: As the number of people living in the house
What happens when
When you buy more pens , do you
think that the total cost will
increase or decrease?
Answer: As you buy more pens ↑, total cost also increases ↑.
When the number of people living in
house decreases, do you think that the
total weekly expense will increase or
decrease?
Answer: As the number of people living in the house
decreases ↓, the weekly expense also decreases ↓.

5. Direct Proportion Now, look at the following tables:
Cost of 1 chocolate (Rs) 5
20 ↑
30 ↑
Cost of 10 chocolates (Rs)
5 x 10 = 50
20 x 10 = 200 ↑
30 x 10 = 300↑
For one to many, we need to multiply
As the cost of 1 chocolate increases ↑, the cost of 10
chocolates also increases ↑ correspondingly.
Cost of 5 Shirts (Rs)
3000
2000
1000 ↓ ↓
Cost of 1 Shirt (Rs) ↓ ↓
As the cost of 5 shirts decreases ↓ , the cost of 1 shirt
also decreases ↓ correspondingly.
For many to one, we need to divide

6. Direct Proportion increase (↑ ) in the other quantity
  When an increase (↑ ) in one quantity brings about an
increase (↑ ) in the other quantity
and similarly a decrease (↓) in one quantity brings about
a decrease (↓) in the other quantity,
then the two quantities are said to be in direct proportion.

7. Some Direct proportion examples:
No of students in a class ↑
No of teachers ↑
Distance travelled by
the car ↑
Time taken by the car ↑
No of chocolates purchased↓
Total expenses ↓
Amount deposited in the bank ↑
Interests for that amount ↑

8. Formula used to solve word problem
In direct proportion,
= Constant
Once we find constant , we can use it to find unknown values

9. Example1: Example: If 6 apples cost 24 rupees, cost of 8 apple is?
Solution: Let a be the cost of 8 apples
Note: When number of apples increases (↑),
the cost of apples also increases (↑).
So, they are in direct proportion.
In direct proportion , Lets find the constant and use it to find a
No. of apples x 6 8
Cost of apples y 24 a
Constant =
Requires complete translation. Will not be present in existing variations PPTs
Now lets find the unknown value a
Ans: Rs. 32

10. Example1: The cost of uniforms for twelve students is Rs.3,000.
How many students can get uniform for Rs.1250.
Solution: Let a be the number of students
Note: When money spent decreases (↓),
the number of uniform also decreases (↓).
So, they are in direct proportion.
In direct proportion , Lets find the constant and use it to find a
Cost of the uniform x
Rs 3000
Rs 1,250
Number of students y 12 a
Refer existing variation word problem file
Constant = 250 and now lets find the unknown value a
Ans: 5 students

11. Example 2: A train covers a distance of 195 km in 3 hrs.
At the same speed, find the distance travelled in 5 hours?
Solution: Let a be the distance travelled
Note: As the distance travelled increases (↑),
time taken also increases (↑ ).
So, they are in direct proportion.
In direct proportion , Lets find the constant and use it to find a
Distance travelled x
195 a
Time Taken y 3 5
Constant = 65 and now lets find the unknown value a
∴ a = 65 x 5 = 325
Ans: 325 km

12. Try These
If 6 children shared 24 pencils equally, then how many pencils are required for 18 children?
A dozen bananas costs Rs. 20. What is the price of 48 bananas?