A number is first decreased by 30% and then, increased by 40%. The resulting number is again increased by 5%. What is the net increase or decrease percentage?

Correct option is C

Given:

Number decreased by 30%

Then increased by 40% and 5%

Formula Used:

Successive percentage = $$x +y + \frac{xy}{100}$$​​

Solution:

Here let the number be 100

Then decreased number = 100 - 30% of 100 = 70

Then the number is increased by 40%

New number  =70 + 40% of 70

= 70+28=98

Resulting number is again increased by 5%

Then increased number is 98 + 5% of 98 = 98 + 4.9 = 102.9

Increase in number = 102.9 -100 = 2.9

Percentage decrease =$$\frac{2.9}{100} \times 100 = 2.9\%$$​​

Alternative Method:

Successive percentage =$$-30+40 + \frac{(-30)(40)}{100}$$​​

= 10-12

=-2%

Now -2% and 5% then resultant number

=$$-2+5+ \frac{(-2)(5)}{100}$$​​

= +3 -0.1

= +2.9%

Here (+) sign means increase