PERCENTAGE SHORTCUT-1 ON VARIOUS MATHEMATICS PROBLEMS
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Shortcut 1: If we increased any value by x % and then decreased by y %. Then the resulting effect in percent will be: “+ x + y + xy /100”.
Various Examples related to this Percentage Short cuts are given below:
Example 1: The price of goods is marks 20% more than the real price by the shopkeeper. After that the shopkeeper allowed a discount of 10%. Now What profit or loss did the shopkeeper will get?
Solution: We solve this as follow by using the percentage shortcut1 as follow:
The Loss (or) Profit he will get is = 20 – 10 + (+20)(-10)/100
= + 8% (profit).
Example 2: Side of the square is increased by 30%. Find the percentage increase in area.
Solution: Here we again use the percentage shortcut 1.
So the increased area percentage = 30 + 30 + (30)(30)/100
= 69 % (increased).
Example 3: Radius of the circle is decreased by 20%. What will be the percent change in area of the circle?
Solution: Therefore by using the percentage shortcut1:
The Percent change in area of circle is= - 20 - 20 + (-20)(-20)/100
= -36% (decreased)
Example 4: The price of a car is increased by 15% than after that again decreased by 15%. What will be the percent change?
Solution: The percent change is = + 15 - 15 + (+15)(-15)/100
= - 2.25 % (decreased)
Example 5: Length of a rectangle is increased by 40% and breadth of the rectangle is decreased by 40%. Find change in area.
Solution: By using the formula of percentage shortcut given above:
The percent change in area of rectangle is= 40 - 40 + (-40)(+40)/100
= -16 %( decreased)
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