Question

a number is decreased by 10% and then increased by 12% find the net increase or decrease percent​

Answer 1

Given,

A number is decreased by 10%

Then increased by 12%

To find,

The net increase or decrease percentage.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the initial number = x

The value after the decrease = x - (x × 10/100) = x - x/10 = 9x/10

The value after the increase = 9x/10 + (9x/10 × 12/100) = 9x/10 + 27x/250 = 225x+27x/250 = 252x/250

Now, the final number is greater than the initial number.

Difference = 252x/250 - x = 2x/250 = x/125

Percentage difference = 100 × (x/125 ÷ x) = 100 × x/125 × 1/x = 0.8%

Hence, the number will increase by 0.8%

Answer 2

SOLUTION

GIVEN

A number is decreased by 10% and then increased by 12%

TO DETERMINE

The net increase or decrease percentage

EVALUATION

Let the number is 100

Now the number is decreased by 10%

So after decrease the new number

$\displaystyle \sf{ = 100 \times \bigg( 1 - \frac{10}{100} \bigg)}$

$\displaystyle \sf{ = 100 \times 0.9}$

$= 90$

Now the number 90 is increased by 12%

So the new number

$\displaystyle \sf{ = 90 \times \bigg( 1 + \frac{12}{100} \bigg)}$

$\displaystyle \sf{ = 90 \times 1.12}$

$= 108$

So initially the number was 100 and finally the number becomes 108

So increase in the number

= 108 - 100

= 8

So the rate of increase

$\displaystyle \sf{ = \frac{8}{100} \times 100 \: \%}$

$= \sf{8 \: \%}$

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