6 replies to this topic

[David]

Here is a little puzzle.



You are in Japan, where tax is added at the till, buying goods priced at 1000 Yen before tax is added.



Tax is 35% , but because you are a good customer, you get a discount of a 30%



QUESTION- Will the ammount you pay be more, or less than, 1000 Yen?







Answer without using a calculator. Tip- it doesn't matter if you apply the discount first, or the addition first - the answer will be the same.

[pyromaniac303]

The answer when I worked both out is less... though I still cant figure out why, as +35% and -30% to the price should surely make it cost more than 1000¥!

Spoiler

1000 + 350 = 1350 (added tax first)
1350 - (1350 x 0.3) = 945

1000 - 300 = 700 (discount first)
700 x 1.35 = 945

[Mortartube]

It's less. 1000 + 35% tax is 1350, take away 30% of 1350 and it is less. I won't post the answer, as I want to let someone else do a bit of the work.

[pyromaniac303]

Oh right, makes more sense now

Edited by pyromaniac303, 25 September 2008 - 11:32 AM.

[David]

The answer when I worked both out is less... though I still cant figure out why, as +35% and -30% to the price should surely make it cost more than 1000¥!

Yeah- thats the odd thing about it. It seems illogical!

[cooperman435]

nah its perfectally logical.

if you get the discount after tax then your getting it knocked off the price plus tax so the discount is more than the tax was origionally even though the tax was a higher %

if done before tax then tax is worked out on the lower amount which doesnt increase it to the origional amount.

[David]

Yeah- its just that people naturally tend to see that and assume its 5% more.

Just for the curious, the "rule" is that if you increase something by a fraction, then decrease it by the next fraction along, the answer will be the same as the number you started with.

EG- Increase something by 1/3 (a third) and then decrease it by a 1/4 (quarter) you get the same answer.

Increase by 1/8 then decrease by 1/9 etc . ( EG 72 plus an eighth (12.5%) = 81 . 81 minus a nineth (11.11%) = 72. )

This, would you beleive, is considered suitable for middle level ability 11 year olds!

Edited by David, 25 September 2008 - 08:06 PM.