Answer
Verified
376.2k+ views
Hint: Learn how to calculate the percentage of any number. Also, learn how to calculate the percentage change of any number. Use the percentage formula to find the value of the increased and decreased number then find the net change in the number.
Formula used: If any number \[a\] is increased by \[x\% \] then the final value of the number will be, \[b = \dfrac{{a(x + 100)}}{{100}}\] where, \[b\] is the final value of the number \[a\] .
If a number \[a\] is changed to a new value \[b\] the change in the number percentage will be, \[\dfrac{{(a \sim b)}}{a} \times 100\% \]
Complete step by step solution:
Here we have given here that a number is first increased by a \[40\% \] and then decreased by \[40\% \] . Now we have to find the final increase or decrease in the original number.
Now we know that if any number \[a\] is increased by \[x\% \] then the final value of the number is, \[b = \dfrac{{a(x + 100)}}{{100}}\] where, \[b\] is the final value of the number \[a\] .
Let’s assume that the number is \[a\] .
Now, if we increase the number by \[40\% \] , the new value of the number will be,
\[ = \dfrac{{a(40 + 100)}}{{100}}\]
\[ = \dfrac{{140}}{{100}}a\]
\[ = \dfrac{7}{5}a\]
Now, if we decrease the new number \[\dfrac{7}{5}a\] by \[40\% \] , the final value of the number will be,
\[ = \dfrac{7}{5}a(\dfrac{{100 - 40}}{{100}})\]
\[ = \dfrac{7}{5}a(\dfrac{{60}}{{100}})\]
\[ = \dfrac{3}{5} \times \dfrac{7}{5}a\]
\[ = \dfrac{{21}}{{25}}a\]
So, we can see that the number is less than the initial value of it.
So, the change in the number is,
\[a - \dfrac{{21}}{{25}}a\]
\[ = \dfrac{4}{{25}}a\]
So, percentage change in the number is,
\[\dfrac{{\dfrac{4}{{25}}a}}{a} \times 100\% \]
\[ = \dfrac{4}{{25}} \times 100\% \]
\[ = 4 \times 4\% \]
\[ = 16\% \]
Hence, the net decrease percent of the number is \[16\% \]
Hence, option (A) is the correct answer.
So, the correct answer is “Option A”.
Note: The change of any number is the difference between its final and initial value. The percentage change is the value of the change in fraction with respect to the initial value times \[100\] .
Always remember that increasing and decreasing a number by the same percentage does not keep the number as it is the value of the number that always changes.
Formula used: If any number \[a\] is increased by \[x\% \] then the final value of the number will be, \[b = \dfrac{{a(x + 100)}}{{100}}\] where, \[b\] is the final value of the number \[a\] .
If a number \[a\] is changed to a new value \[b\] the change in the number percentage will be, \[\dfrac{{(a \sim b)}}{a} \times 100\% \]
Complete step by step solution:
Here we have given here that a number is first increased by a \[40\% \] and then decreased by \[40\% \] . Now we have to find the final increase or decrease in the original number.
Now we know that if any number \[a\] is increased by \[x\% \] then the final value of the number is, \[b = \dfrac{{a(x + 100)}}{{100}}\] where, \[b\] is the final value of the number \[a\] .
Let’s assume that the number is \[a\] .
Now, if we increase the number by \[40\% \] , the new value of the number will be,
\[ = \dfrac{{a(40 + 100)}}{{100}}\]
\[ = \dfrac{{140}}{{100}}a\]
\[ = \dfrac{7}{5}a\]
Now, if we decrease the new number \[\dfrac{7}{5}a\] by \[40\% \] , the final value of the number will be,
\[ = \dfrac{7}{5}a(\dfrac{{100 - 40}}{{100}})\]
\[ = \dfrac{7}{5}a(\dfrac{{60}}{{100}})\]
\[ = \dfrac{3}{5} \times \dfrac{7}{5}a\]
\[ = \dfrac{{21}}{{25}}a\]
So, we can see that the number is less than the initial value of it.
So, the change in the number is,
\[a - \dfrac{{21}}{{25}}a\]
\[ = \dfrac{4}{{25}}a\]
So, percentage change in the number is,
\[\dfrac{{\dfrac{4}{{25}}a}}{a} \times 100\% \]
\[ = \dfrac{4}{{25}} \times 100\% \]
\[ = 4 \times 4\% \]
\[ = 16\% \]
Hence, the net decrease percent of the number is \[16\% \]
Hence, option (A) is the correct answer.
So, the correct answer is “Option A”.
Note: The change of any number is the difference between its final and initial value. The percentage change is the value of the change in fraction with respect to the initial value times \[100\] .
Always remember that increasing and decreasing a number by the same percentage does not keep the number as it is the value of the number that always changes.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE