Math Percentage Problem

  Mary_S 13:14 13 Sep 2010

Consider the following. The price of a pen was 1.40 pence on Monday. On Tuesday it rose to 63.89.
My calculation is (new value - old value)/ old value * 100 so (63.89-1.40)/1.40 * 100 = 4464%. The price of the pen has had an increase of 4464 %.
Now someone has presented the following calculation, which ot me is wrong.
(63.89-1.4)63.89 * 100 which results in a 98% increase. To me the latter is wrong. Can someone tell if its wrong or does it depend on how you interept the data. If the latter is a valid calculation please do explain why?
Thank You

  babybell 13:40 13 Sep 2010

If the pen was 1.40, a 100% increase would mean it was 2.80, therefor, a 98% increase would NOT be correct.

  lotvic 14:35 13 Sep 2010

If I do it this way

1% of 1.40 = 0.014
each increment rise of 0.014p is 1% more (1.40p + 0.014p = 1.414p means price has risen 1%)
The pen costs 62.49p more on Tues (63.89p - 1.40p = 62.49p)
62.49p price increase is 62.49p / 0.014 = 4463.5714% increase

so a 98% increase would be 98 * 0.014 which is 1.372p increase in price
making the price of pen 1.40p + 1.372p which = 2.772p

  skeletal 17:05 13 Sep 2010

I agree with babybell and lotvic.

It does not depend on how you interpret the data.

It does depend on how you STATE the data.

If you say “The price of the pen has increased by…” then this means that you base your calculation on the first price, in this case 1.40 pence. The rest of your first paragraph then follows (i.e. 1.4 is the denominator).

If, following the increase, the price dropped back to 1.40, you then move the 63.89 to the denominator and get (63.89-1.4)/63.89*100 = 97.81% DECREASE (from the new price).

I find percentages a bit confusing once they move outside the 0-100% range; people’s language can get a bit woolly like: “The price is now 110%”, or “It’s gone up 100%”. Can we be sure the speaker really means what they are saying? Not forgetting X-factor judges who “Agree 1 million per cent”.


  lotvic 18:46 13 Sep 2010

if the 100% price is 63.89p then 0.6389p is 1%
97.81% of 63.89p is (63.89p *97.81)/100 which gives 62.49p

so a 97.81% decrease from 63.89p means the pen would be priced at 2.19% of 63.89p
2.19% of 63.89p is
(63.89*2.19)/100 which is 1.40p

or if you like, (0.6389p * 2.19) which is 1.40p

(rounded up to 2 decimal places)

  Grey Goo 21:30 13 Sep 2010

Just think, the country may only be in debt by three and six, instead of a trillion or two depending on how it's calculated.

  BRYNIT 22:14 13 Sep 2010

the calculation should be

(63.89/1.4)*100 = 4563.5714%

  skeletal 22:20 13 Sep 2010

fourm member: Grrrrrrr.....!!

Mary_S: “Now someone has...”. Is this “someone” an MP or who works in taxation by any chance??!!

Ducks and runs for the door...


  lotvic 23:11 13 Sep 2010

Try this sum
The price of a pen was 100 pence on Monday. On Tuesday it rose to 120 pence
The price of the pen has had an increase of ?%

  BRYNIT 23:55 13 Sep 2010


No I can't work that one out you'll just have to do it out yourself :)

  lotvic 00:14 14 Sep 2010

I shall refrain from letting you do any shopping for bargains in the sales ;@}

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