Variations word problem

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

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

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

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

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

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?