A number is increased by 10% and then it is decreased by 10% find the net decrease percent

A number is increased by 10 per cent. Then it is decreased by 20 per cent. If the final value of the number is 528, then what is the initial value of the number?

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A number is increased by 10 per cent. Then it is decreased by 20 per cent. If the final value of the number is 528, then what is the initial value of the number?
Answer (Detailed Solution Below)
A number is increased by \[10\% \] and then decreased by \[10\% ,\] find the net increase or decrease per cent.A) \[15\% \]B) \[1\% \]C) \[13\% \]D) \[17\% \]
When a number is first increased by 10% and then reduced by 10% the number?
Is decreased by 10% and then increased by 10% the number so obtained is 10 less than the original number What was the original number?
How do you decrease a number by 10%?
How do you increase a number by 10%?

IB ACIO Grade II Previous Paper 8 (Held on: 19 Feb 2021 Shift 1)

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Answer (Detailed Solution Below)

Option 3 : 600

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Given:

Increase in number = 10%

Decrease in number = 20%

Calculations:

Let the number be 100x.

After 10% is increased,

New number = 100x × 100x + 10%

⇒ 110x

After 20% decreased,

New number = 110x - 110x × 20%

⇒ 110x - 22x

⇒ 88x

88x = 528

⇒ x = 6

So, 100x = 600

∴ The initial value of the number is 600.

Shortcut Trick

Let the initial number be 100%.

Overall percentage change = a% + b% + (ab/100)%

⇒ 10 - 20 + (10)(-20)/100

⇒ -10 -2

⇒ -12%

100% - 12% → 528

⇒ 88% → 528

⇒ 1% → 6

⇒ 100% → 600

∴ The initial value of the number is 600.

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A number is increased by \[10\% \] and then decreased by \[10\% ,\] find the net increase or decrease per cent.A) \[15\% \]B) \[1\% \]C) \[13\% \]D) \[17\% \]

Answer

Verified

Hint: To solve this question, first we will assume that the number be \[100,\] and according to the question, we will first increase the number by \[10\% \], then we will decrease the number by \[10\% \]. Then after that we will find whether we get net increase or decrease per cent.

Complete step-by-step answer:
We have been given that a number is increased by \[10\% \] and then decreased by \[10\% ,\] we need to find the net increase or decrease per cent.
First of all, we will assume the number. So, let the number be \[100.\]
We have been given in the question that firstly, the number is increased by \[10{\text{ }}\% .\]
\[
   \Rightarrow 100{\text{ }} + {\text{ }}\dfrac{{\left( {100 \times 10} \right)}}{{100}} \\
   = 100{\text{ }} + {\text{ }}10 \\
   = 110 \\
\]
Then, we have been given in the question that secondly, the number is decreased by \[10\% .\]
\[
   \Rightarrow 110{\text{ - }}\dfrac{{\left( {110 \times 10} \right)}}{{100}} \\
   = 110{\text{ - 11}} \\
   = 99 \\
\]
Now, we know that, the net increase or decrease percentage \[ = \] (Original Number \[ - \] New Number)\[ \times \dfrac{{100}}{{100}}\]
where, the original number \[ = {\text{ }}100\]
and the new number \[ = {\text{ }}99\]
On putting the values in the above formula, we get
Net increase or decrease percentage
\[
   = {\text{ }}\left( {100{\text{ }} - {\text{ }}99} \right) \times \dfrac{{100}}{{100}} \\
   = (1) \times \dfrac{{100}}{{100}} \\
   = \dfrac{{100}}{{100}} \\
   = {\text{ }}1{\text{ }}\% \\
\]
So, we get the net decrease, which is \[1\% .\]
So, the correct answer is “Option B”.

Note: Students should take care, that in the solution, here we have assumed the number be \[100.\] Then we have applied the first condition i.e., increased by \[10\% \] on \[100,\] we get \[110.\] Now when we have applied the second condition i.e., decreased by \[10\% ,\] it is important for students to note that we have applied second condition on \[110\] not on \[100.\]

When a number is first increased by 10% and then reduced by 10% the number?

Hint-In this question we are given that a number is first increased by 10% and then reduced by 10%. For this, let the number at the start be 100 and apply the directions given in question to get the result. Hence the number is decreased by 1%. Therefore, the correct is B.

Is decreased by 10% and then increased by 10% the number so obtained is 10 less than the original number What was the original number?

This is Expert Verified Answer Number increase by 10% and it becomes 110. 2nd we have to decrease 10% from 110, and 10 % of 110 is 11. so we have remaining 99. when 1 decrease it is 100.

How do you decrease a number by 10%?

One of the easiest ways to determine a 10 percent discount is to divide the total sale price by 10 and then subtract that from the price. You can calculate this discount in your head. For a 20 percent discount, divide by ten and multiply the result by two.

How do you increase a number by 10%?

How do I calculate a 10% increase? Divide the number you are adding the increase to by 10. Alternatively multiply the value by 0.1. Add the product of the previous step to your original number.

Increase by 10