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Three times a number is 200% increase in the number, then one third of the same number is 200% decrease in the number. Is the following statement true or false

Solution.

If the number is x then three times the number = 3x

Therefore the gain% is = [(3x - x)/x] × 100

= 200%

If the number is decreased to x/3 then the decrease percentage is calculated as:

Decrease = x - x/3 = 2x/3

Decrease % = [2x/3]/x 100

= 200/3 %

= 66 2/3%

Hence the given statement is false.

✦ Try This: Thrice the number 225 is an increase of 200% while a decrease one third of the same number is 66 ⅔% decrease in the number. Is the statement true or false?

The number is 225 then three times the number = 675

Therefore the gain% is = [(675 - 225)/225] × 100 = [450/225] × 100 = 200%

If the number is decreased to 225/3 = 75 then the decrease percentage is calculated as:

Decrease = 225 - 75 = 150

Decrease % = [150/225] x 100 = (10/15) x 100 = (2/3) x 100 = 66 ⅔%

Hence Statement is true

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 8

NCERT Exemplar Class 8 Maths Chapter 9 Problem 52

Three times a number is 200% increase in the number, then one third of the same number is 200% decrease in the number. Is the following statement true or false

Summary:

The statement “Three times a number is a 200% increase in the number, then one third of the same number is 200% decrease in the number.” is a False statement

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