Adding a percentage to a number and then subtracting the same percentage to get the same number

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up vote
1
down vote

favorite

I wonder if you can help me?
I have found similar answers to this question but they don't seem to work.

I am after a formula or an excel formula so I can add a percentage to a number, then when I discount the same percentage off the larger figure I get back to exactly the same figure.

The reason for this is because I sell products at a price, some of my customers have special terms when they purchase so I add a percentage onto the selling price to cover these terms. Then when this percentage is discounted off the inflated cost, I need the selling total to go back to the original selling price.

For instance:
If I sell at £1.00,
Customer A has terms of 10%, so I need to add 10% onto 1.00, which is £1.10.
Then when I take 10% off £1.10, which is £0.11p, this returns to £0.99p, which is lower than my original selling price.

If anyone could help with a formula to explain the answer it would be amazing!
I would need the formula to work with different selling prices and different percentages.

Thanks in advance!
Adam

algebra-precalculus percentages

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edited Jul 26 at 9:34

Especially Lime

19.1k22252

asked Jul 26 at 9:23

AdamF

82

add a comment | 

up vote
1
down vote

favorite

I wonder if you can help me?
I have found similar answers to this question but they don't seem to work.

I am after a formula or an excel formula so I can add a percentage to a number, then when I discount the same percentage off the larger figure I get back to exactly the same figure.

The reason for this is because I sell products at a price, some of my customers have special terms when they purchase so I add a percentage onto the selling price to cover these terms. Then when this percentage is discounted off the inflated cost, I need the selling total to go back to the original selling price.

For instance:
If I sell at £1.00,
Customer A has terms of 10%, so I need to add 10% onto 1.00, which is £1.10.
Then when I take 10% off £1.10, which is £0.11p, this returns to £0.99p, which is lower than my original selling price.

If anyone could help with a formula to explain the answer it would be amazing!
I would need the formula to work with different selling prices and different percentages.

Thanks in advance!
Adam

algebra-precalculus percentages

share|cite|improve this question

edited Jul 26 at 9:34

Especially Lime

19.1k22252

asked Jul 26 at 9:23

AdamF

82

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

I wonder if you can help me?
I have found similar answers to this question but they don't seem to work.

I am after a formula or an excel formula so I can add a percentage to a number, then when I discount the same percentage off the larger figure I get back to exactly the same figure.

The reason for this is because I sell products at a price, some of my customers have special terms when they purchase so I add a percentage onto the selling price to cover these terms. Then when this percentage is discounted off the inflated cost, I need the selling total to go back to the original selling price.

For instance:
If I sell at £1.00,
Customer A has terms of 10%, so I need to add 10% onto 1.00, which is £1.10.
Then when I take 10% off £1.10, which is £0.11p, this returns to £0.99p, which is lower than my original selling price.

If anyone could help with a formula to explain the answer it would be amazing!
I would need the formula to work with different selling prices and different percentages.

Thanks in advance!
Adam

algebra-precalculus percentages

share|cite|improve this question

edited Jul 26 at 9:34

Especially Lime

19.1k22252

asked Jul 26 at 9:23

AdamF

82

I wonder if you can help me?
I have found similar answers to this question but they don't seem to work.

I am after a formula or an excel formula so I can add a percentage to a number, then when I discount the same percentage off the larger figure I get back to exactly the same figure.

The reason for this is because I sell products at a price, some of my customers have special terms when they purchase so I add a percentage onto the selling price to cover these terms. Then when this percentage is discounted off the inflated cost, I need the selling total to go back to the original selling price.

For instance:
If I sell at £1.00,
Customer A has terms of 10%, so I need to add 10% onto 1.00, which is £1.10.
Then when I take 10% off £1.10, which is £0.11p, this returns to £0.99p, which is lower than my original selling price.

If anyone could help with a formula to explain the answer it would be amazing!
I would need the formula to work with different selling prices and different percentages.

Thanks in advance!
Adam

algebra-precalculus percentages

share|cite|improve this question

edited Jul 26 at 9:34

Especially Lime

19.1k22252

asked Jul 26 at 9:23

AdamF

82

share|cite|improve this question

share|cite|improve this question

edited Jul 26 at 9:34

Especially Lime

19.1k22252

edited Jul 26 at 9:34

Especially Lime

19.1k22252

edited Jul 26 at 9:34

Especially Lime

19.1k22252

19.1k22252

asked Jul 26 at 9:23

AdamF

82

asked Jul 26 at 9:23

AdamF

82

asked Jul 26 at 9:23

AdamF

82

82

add a comment | 

add a comment | 

2 Answers
2

active

oldest

votes

up vote
0
down vote



accepted

You will need to modify the percentages. If you add $x%$ to a price $P$ then your new price is $Q=P+fracPx100$. You now want to subtract $fracPx100$ from $Q$, but that is $x%$ of $P$, not $x%$ of $Q$. As a proportion of $Q$, it is $$fracfracx1001+fracx100=fracx100+x,$$
so this means that instead of subtracting $x%$ you need to subtract $y%$ of $Q$, where $$y=frac100x100+x.$$
For example, if you added $10%$ you must subtract $frac1000110%=9.overline09%$.

share|cite|improve this answer

answered Jul 26 at 9:33

Especially Lime

19.1k22252

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  No problem :) You need to subtract $frac1650116.5%$, which is about $14.164%$.
  – Especially Lime
  Jul 26 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  eeeek. So £1.56 * 1.165 = £1.8174p, which is 16.5% increase of £1.56. Then to deduct 16.5% from £1.8174 I need to subtract 14.164% from £1.8174? Doesn't that leave me with £1.5919203p ? I'm so confused haha
  – AdamF
  Jul 26 at 11:12
  

  
  
  
  

add a comment | 

up vote
0
down vote

If you take $99%$ off $€100$, you get $€1$. Then if you add $99%$ to $€1$, you get $€1.99$, much less than $€100$ because you didn't consider $99%$ of the same thing.

In general adding $x%$ is multiplying by $1+frac x100$, so if you want the reverse of that you need to divide by $1+frac x100$, which is the same as multiplying by $frac11+frac x100$. Now

$$frac11+frac x100=1-fracx100+x$$
so the reverse of adding $x%$ is subtracting $(100cdot fracx100+x)%$

---

Example: $x=10$; the reverse operation of $+10%$ is $-(100cdot frac10100+10)%simeq -9.09%$

share|cite|improve this answer

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  sorry I meant £1.8174 not £1.18174
  – AdamF
  Jul 26 at 11:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you subtract the same percentage you don't get back to the initial amount. To get back to the initial amount after an increase by $x%$, you need a decrease by $frac100x100+x%$.
  – Arnaud Mortier
  Jul 26 at 16:28
  

  
  
  
  

add a comment | 

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
0
down vote



accepted

You will need to modify the percentages. If you add $x%$ to a price $P$ then your new price is $Q=P+fracPx100$. You now want to subtract $fracPx100$ from $Q$, but that is $x%$ of $P$, not $x%$ of $Q$. As a proportion of $Q$, it is $$fracfracx1001+fracx100=fracx100+x,$$
so this means that instead of subtracting $x%$ you need to subtract $y%$ of $Q$, where $$y=frac100x100+x.$$
For example, if you added $10%$ you must subtract $frac1000110%=9.overline09%$.

share|cite|improve this answer

answered Jul 26 at 9:33

Especially Lime

19.1k22252

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  No problem :) You need to subtract $frac1650116.5%$, which is about $14.164%$.
  – Especially Lime
  Jul 26 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  eeeek. So £1.56 * 1.165 = £1.8174p, which is 16.5% increase of £1.56. Then to deduct 16.5% from £1.8174 I need to subtract 14.164% from £1.8174? Doesn't that leave me with £1.5919203p ? I'm so confused haha
  – AdamF
  Jul 26 at 11:12
  

  
  
  
  

add a comment | 

up vote
0
down vote



accepted

You will need to modify the percentages. If you add $x%$ to a price $P$ then your new price is $Q=P+fracPx100$. You now want to subtract $fracPx100$ from $Q$, but that is $x%$ of $P$, not $x%$ of $Q$. As a proportion of $Q$, it is $$fracfracx1001+fracx100=fracx100+x,$$
so this means that instead of subtracting $x%$ you need to subtract $y%$ of $Q$, where $$y=frac100x100+x.$$
For example, if you added $10%$ you must subtract $frac1000110%=9.overline09%$.

share|cite|improve this answer

answered Jul 26 at 9:33

Especially Lime

19.1k22252

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  No problem :) You need to subtract $frac1650116.5%$, which is about $14.164%$.
  – Especially Lime
  Jul 26 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  eeeek. So £1.56 * 1.165 = £1.8174p, which is 16.5% increase of £1.56. Then to deduct 16.5% from £1.8174 I need to subtract 14.164% from £1.8174? Doesn't that leave me with £1.5919203p ? I'm so confused haha
  – AdamF
  Jul 26 at 11:12
  

  
  
  
  

add a comment | 

up vote
0
down vote



accepted

up vote
0
down vote



accepted

You will need to modify the percentages. If you add $x%$ to a price $P$ then your new price is $Q=P+fracPx100$. You now want to subtract $fracPx100$ from $Q$, but that is $x%$ of $P$, not $x%$ of $Q$. As a proportion of $Q$, it is $$fracfracx1001+fracx100=fracx100+x,$$
so this means that instead of subtracting $x%$ you need to subtract $y%$ of $Q$, where $$y=frac100x100+x.$$
For example, if you added $10%$ you must subtract $frac1000110%=9.overline09%$.

share|cite|improve this answer

answered Jul 26 at 9:33

Especially Lime

19.1k22252

You will need to modify the percentages. If you add $x%$ to a price $P$ then your new price is $Q=P+fracPx100$. You now want to subtract $fracPx100$ from $Q$, but that is $x%$ of $P$, not $x%$ of $Q$. As a proportion of $Q$, it is $$fracfracx1001+fracx100=fracx100+x,$$
so this means that instead of subtracting $x%$ you need to subtract $y%$ of $Q$, where $$y=frac100x100+x.$$
For example, if you added $10%$ you must subtract $frac1000110%=9.overline09%$.

share|cite|improve this answer

answered Jul 26 at 9:33

Especially Lime

19.1k22252

share|cite|improve this answer

share|cite|improve this answer

answered Jul 26 at 9:33

Especially Lime

19.1k22252

answered Jul 26 at 9:33

Especially Lime

19.1k22252

answered Jul 26 at 9:33

Especially Lime

19.1k22252

19.1k22252

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  No problem :) You need to subtract $frac1650116.5%$, which is about $14.164%$.
  – Especially Lime
  Jul 26 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  eeeek. So £1.56 * 1.165 = £1.8174p, which is 16.5% increase of £1.56. Then to deduct 16.5% from £1.8174 I need to subtract 14.164% from £1.8174? Doesn't that leave me with £1.5919203p ? I'm so confused haha
  – AdamF
  Jul 26 at 11:12
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  No problem :) You need to subtract $frac1650116.5%$, which is about $14.164%$.
  – Especially Lime
  Jul 26 at 10:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  eeeek. So £1.56 * 1.165 = £1.8174p, which is 16.5% increase of £1.56. Then to deduct 16.5% from £1.8174 I need to subtract 14.164% from £1.8174? Doesn't that leave me with £1.5919203p ? I'm so confused haha
  – AdamF
  Jul 26 at 11:12
  

  
  
  
  

Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
– AdamF
Jul 26 at 10:43

Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
– AdamF
Jul 26 at 10:43

No problem :) You need to subtract $frac1650116.5%$, which is about $14.164%$.
– Especially Lime
Jul 26 at 10:52

No problem :) You need to subtract $frac1650116.5%$, which is about $14.164%$.
– Especially Lime
Jul 26 at 10:52

eeeek. So £1.56 * 1.165 = £1.8174p, which is 16.5% increase of £1.56. Then to deduct 16.5% from £1.8174 I need to subtract 14.164% from £1.8174? Doesn't that leave me with £1.5919203p ? I'm so confused haha
– AdamF
Jul 26 at 11:12

eeeek. So £1.56 * 1.165 = £1.8174p, which is 16.5% increase of £1.56. Then to deduct 16.5% from £1.8174 I need to subtract 14.164% from £1.8174? Doesn't that leave me with £1.5919203p ? I'm so confused haha
– AdamF
Jul 26 at 11:12

add a comment | 

up vote
0
down vote

If you take $99%$ off $€100$, you get $€1$. Then if you add $99%$ to $€1$, you get $€1.99$, much less than $€100$ because you didn't consider $99%$ of the same thing.

In general adding $x%$ is multiplying by $1+frac x100$, so if you want the reverse of that you need to divide by $1+frac x100$, which is the same as multiplying by $frac11+frac x100$. Now

$$frac11+frac x100=1-fracx100+x$$
so the reverse of adding $x%$ is subtracting $(100cdot fracx100+x)%$

---

Example: $x=10$; the reverse operation of $+10%$ is $-(100cdot frac10100+10)%simeq -9.09%$

share|cite|improve this answer

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  sorry I meant £1.8174 not £1.18174
  – AdamF
  Jul 26 at 11:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you subtract the same percentage you don't get back to the initial amount. To get back to the initial amount after an increase by $x%$, you need a decrease by $frac100x100+x%$.
  – Arnaud Mortier
  Jul 26 at 16:28
  

  
  
  
  

add a comment | 

up vote
0
down vote

If you take $99%$ off $€100$, you get $€1$. Then if you add $99%$ to $€1$, you get $€1.99$, much less than $€100$ because you didn't consider $99%$ of the same thing.

In general adding $x%$ is multiplying by $1+frac x100$, so if you want the reverse of that you need to divide by $1+frac x100$, which is the same as multiplying by $frac11+frac x100$. Now

$$frac11+frac x100=1-fracx100+x$$
so the reverse of adding $x%$ is subtracting $(100cdot fracx100+x)%$

---

Example: $x=10$; the reverse operation of $+10%$ is $-(100cdot frac10100+10)%simeq -9.09%$

share|cite|improve this answer

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  sorry I meant £1.8174 not £1.18174
  – AdamF
  Jul 26 at 11:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you subtract the same percentage you don't get back to the initial amount. To get back to the initial amount after an increase by $x%$, you need a decrease by $frac100x100+x%$.
  – Arnaud Mortier
  Jul 26 at 16:28
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

If you take $99%$ off $€100$, you get $€1$. Then if you add $99%$ to $€1$, you get $€1.99$, much less than $€100$ because you didn't consider $99%$ of the same thing.

In general adding $x%$ is multiplying by $1+frac x100$, so if you want the reverse of that you need to divide by $1+frac x100$, which is the same as multiplying by $frac11+frac x100$. Now

$$frac11+frac x100=1-fracx100+x$$
so the reverse of adding $x%$ is subtracting $(100cdot fracx100+x)%$

---

Example: $x=10$; the reverse operation of $+10%$ is $-(100cdot frac10100+10)%simeq -9.09%$

share|cite|improve this answer

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

If you take $99%$ off $€100$, you get $€1$. Then if you add $99%$ to $€1$, you get $€1.99$, much less than $€100$ because you didn't consider $99%$ of the same thing.

In general adding $x%$ is multiplying by $1+frac x100$, so if you want the reverse of that you need to divide by $1+frac x100$, which is the same as multiplying by $frac11+frac x100$. Now

$$frac11+frac x100=1-fracx100+x$$
so the reverse of adding $x%$ is subtracting $(100cdot fracx100+x)%$

---

Example: $x=10$; the reverse operation of $+10%$ is $-(100cdot frac10100+10)%simeq -9.09%$

share|cite|improve this answer

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

share|cite|improve this answer

share|cite|improve this answer

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

answered Jul 26 at 9:32

Arnaud Mortier

18.6k22159

18.6k22159

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  sorry I meant £1.8174 not £1.18174
  – AdamF
  Jul 26 at 11:04
  

  
  
  
  


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  If you subtract the same percentage you don't get back to the initial amount. To get back to the initial amount after an increase by $x%$, you need a decrease by $frac100x100+x%$.
  – Arnaud Mortier
  Jul 26 at 16:28
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
  – AdamF
  Jul 26 at 10:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  sorry I meant £1.8174 not £1.18174
  – AdamF
  Jul 26 at 11:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If you subtract the same percentage you don't get back to the initial amount. To get back to the initial amount after an increase by $x%$, you need a decrease by $frac100x100+x%$.
  – Arnaud Mortier
  Jul 26 at 16:28
  

  
  
  
  

Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
– AdamF
Jul 26 at 10:46

Thank you so much for your time commenting on my post! I'm still a bit confused, maths isn't my strong point I'm afraid. How would this work If I used as selling price of £1.56, added on 16.5% and then wanted to subtract 16.5% from £1.18174 to get back to £1.56? How would that work in that formula you supplied? Thanks in advance!
– AdamF
Jul 26 at 10:46

sorry I meant £1.8174 not £1.18174
– AdamF
Jul 26 at 11:04

sorry I meant £1.8174 not £1.18174
– AdamF
Jul 26 at 11:04

If you subtract the same percentage you don't get back to the initial amount. To get back to the initial amount after an increase by $x%$, you need a decrease by $frac100x100+x%$.
– Arnaud Mortier
Jul 26 at 16:28

If you subtract the same percentage you don't get back to the initial amount. To get back to the initial amount after an increase by $x%$, you need a decrease by $frac100x100+x%$.
– Arnaud Mortier
Jul 26 at 16:28

add a comment | 

 

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