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Exercise 5a - Example 		Home
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Unitary Method:
If the price of 25 pens are given, we can calculate the price of 10 pens. This method is called Unitary Method.

Example 1: A shop owner bought 80 pens from a wholesaler at the price of $75 for 100 pens. How much does the shop owner pay for the pens?
Price 100 pens = $75
Price of 1 pen = 75/100 = $0.75
Price of 80 pens = $0.75 x 80 = $60

Example 2: Cost of 22 bags is $198. How many bags can be bought for $153.00?
Price 22 bags = $198
Price of 1 bag = 198/22 = $9.00
Number of bags for $153 = 153/9 = 17

Direct Variation:
Let us take the price of shoes. 2 shoes cost $50, 5 shoes at the same rate cost $125, 9 shoes at the same rate cost $225 and 3 shoes at the same rate cost $75. More number of shoes cost more money and less number of shoes cost less money.

The number of shoes and cost of shoes are in direct variations.
Direct variation: Two quantities are said to be in direct variation if one quantity increase, then the other also increase or when one quantity decreases, the other also decreases
Example 3: Cost of 15 books is $195. What is the cost of 20 books?
Number of books Cost of books in dollars
15 195
20 ?
Number of books increases the cost also increases. Here number of books and the cost are in direct variation.
Multiplication factor = 20
15 		 
Cost of 20 books = 20 x 195
15 		= $260


Inverse Variation:
If 12 men can do some work in 10 days, 24 men can do the same work in 5 days and 6 men will finish the same work in 20 days. More men finish the work in less days whereas less men will take more days to finish the same work. Here number of men and number of days are in inverse variation.
Inverse variation: Two quantities are said to be in inverse variation if one quantity increase, then the other decreases or when one quantity decreases, the other increases.
Example 4: If the speed is 35 miles/hour it will take 3 hours to cover the distance. i)How long it will take if the speed is 15 miles /hour to cover the same distance? ii)Calculate the speed to cover the same distance in an hour.
i)
Speed in miles/hour Time in hours
35 3
15 ?
As the speed increases the time required decreases . Here speed and time to cover the distance are in inverse variation.
Multiplication factor = 35
15 		 
Time required if the speed is 15 miles/hour = 35 x 3
15 		= 7 hours

ii)
Speed in miles/hr Time in hours
35 3
? 1
Multiplication factor = 3
1 		 
Speed to cover the same distance in 1 hour = 3 x 35
1 		= 105 miles/hour


Example 5: 20 men did some work for 2 days and got paid a total of $4800. How much pay did 15 men get if they work for 6 days the same amount of work?
Number of men Time in daysPay in dollars
20 24,800
15 6?
Number of men more, the pay is also more. Number of men and pay are in direct variation.
Multiplication factor = 15
20 		 
As days of work increase, pay will also increases. Time and pay in direct variation.
Multiplication factor = 6
2 		 
Pay for 15 men working for 6 days = 15 x
20 		6 x 4800
2 		= $10,800


Example 6: 20 men did some work for 4 days working 6 hours a day. In how many days can 16 men do the same work, if they work for 10 hours per day?
Number of men hours per dayTime in days
20 64
16 10?
Number of men more, time required to finish the work less. Number of men and time required are in inverse variation.
Multiplication factor = 20
16 		 
As number of hours to work increase, day required to finish the work decreases. Hours per day and number of days required are in inverse variation.
Multiplication factor = 6
10 		 
Pay for 15 men working for 6 days = 20 x
16 		6 x 4
10 		= 3 days


Example 7: 20 men cleaned 35,000 sq.ft. working 6 hours. In what time 16 men can clean an area of 56,000 sq.ft.?
Number of men areaTime
20 35,0006
16 56,000?
Number of men more, time required to finish the work less. Number of men and time required are in inverse variation.
Multiplication factor = 20
16 		 
As area to be cleaned increases, number of hours required also increases. Hours and area to be cleaned are in direct variation.
Multiplication factor = 56,000
35,000 		 
Time = 20 x
16 		56,000 x 6
35,000 		= 12 hours




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