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A number when increased by 50 %', gives 2970. The number is:
1980
5940
3960
990
1980
50% increase means 23тАЛ of the original number. So, original number = 2970├Ч32тАЛ=1980.
Increased value = 2970, Percentage increase = 50%
Original=1+100PercentageтАЛIncreased┬аValueтАЛ
50% increase means 23тАЛ of the original number. So, original number = 2970├Ч32тАЛ=1980.
Students often calculate 50% of 2970 and subtract it, getting 2970тИТ1485=1485, which incorrectly treats 2970 as the base.
Define the Variable
Let the original number be x.
x
Set up the Equation
Increasing x by 50% means adding 50% of x to x, which equals 2970.
x+10050тАЛx=2970
Simplify the Equation
Combine terms to get 1.5x=2970 or in fraction form:
23тАЛx=2970
Solve for the Original Number
Multiply both sides by 2 and divide by 3 to find x.
x=32970├Ч2тАЛ=1980
A is correct because calculating 32тАЛ of 2970 yields the original number 1980.
In Profit & Loss questions, an increase of 50% is equivalent to a Cost Price to Selling Price ratio of 2:3, where CP=32тАЛSP.
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