Question

How do you increase 40 by 10%?

Answer 1

Hint: We find the formula for the increase of a particular number by a particular percentage. We place the value of 40 and the percentage of 10 to find the increased value. We also use the concept of 100 to verify the increased value at the end.

Complete step-by-step solution:
There is a given number x and the percentage value of y by which we have to increase the value of x.
The increased value of the number x will be $x\left( 1+\dfrac{y}{100} \right)$.
The increase of the number was $\dfrac{xy}{100}$.
The y% increase tells us about the increment value out of 100.
Now we place the values for $x=40,y=10$.
The increased value is $40\left( 1+\dfrac{10}{100} \right)$. Solving the addition part inside the bracket we get
$40\left( 1+\dfrac{10}{100} \right)=40\left( 1+\dfrac{1}{10} \right)=40\left( \dfrac{11}{10} \right)$.
Now doing the multiplication we get $40\left( \dfrac{11}{10} \right)=\dfrac{40\times 11}{10}=44$.
We can also increase a number by a percentage by converting the percent to a decimal.
So, the increase is 10% which gives $\dfrac{10}{100}=.1$. Multiplying with 40 we get $40\times .1=4$.
The increment is 4. Increased value is $40+4=44$.

Note: We can also use the concept of 100 to evaluate the increased value of the number. When the main number is 100 then the increase in the number is 10 out of 100 which gives us a new increased value of $100+10=110$.
The main value of 100 gives increased value of 110. Using a unitary system, we get the main value of 40 will give $40\left( \dfrac{110}{100} \right)=\dfrac{40\times 110}{100}=44$.