1. Variations word problem

2. Variation formula used to solve word problem
In direct variation,
= Constant
In inverse variation, xy = constant
Once we find constant , we can use it to find unknown values

3. Example1: 7 men can complete a work in 52 days.
In how many days will 13 men finish the same work?
Solution: Let a be the number of days
Note: As the number of men increases (↑),
number of days decreases (↓),
So they are in Inverse variation.
In Inverse variation xy =constant, Lets find the constant and use it to find a
xy = 7 * 52= 364 = constant
Constant=364 and now lets find the unknown value a
∴ 13 x a = 364
Number of men x 7 13
Number of days y 52 a
Ans: 28 days

4. Lets use x for bigger number and y for smaller number
Example2: 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 variation.
In direct variation , 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
Constant = 250 and now lets find the unknown value a
Lets use x for bigger number and
y for smaller number
Ans: 5 students

5. Example 3: 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 variation.
In direct variation , 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

6. Example 4: A book contains 120 pages. Each page has 35 lines.
How many pages will the book contain if every page has 24 lines per page?
Solution: Let the Number of pages to find be a
Note: As the number of lines per page decreases (↓),
number of pages will increases (↑ ).
So, they are in Inverse variation.
In Inverse variation xy=constant , Lets find the constant and use it to find a
xy = 35 * 120= 4200 = constant
Constant=4200 and now lets find the unknown value a
Number of lines x 35 24
Number of pages y
120 a
24 x a = 4200
Ans : 175 pages

7. Try these
1. Vijay’s salary vary directly as the number of hours that he
works. If his salary for 3 hours is Rs-150, how much will he earn for 30 hours?
2. If 150 persons can consume a certain amount of food in
2 months, in how many months can 100 persons consume the
same amount of food?