Bats And Balls

[Khandro]

A bat and a ball cost £1.10 in total. The bat costs £1 more than the ball. How much does the ball cost ?

[mallyh]

5p

[Khandro]

mallyh; I think you must be right. I don't know the answer, but I know it isn't the 'obvious' 10p. my first thought.

Please explain. 🙂

[mallyh]

the bat cost £1 MORE so the ball is 5p and the bat is 5p plus £1

[mallyh]

mr mally told me this as i'm hopeless at this type of question x

[sddsddean]

BAT + BALL = 110

BAT = BALL +100

therefore BALL+100 + BALL= 110

therefore 2BALL = 10

therefore BALL = 5 and BAT = 105

QED

 

[elliemay1]

If the bat is £1 more then take that away from the total to leave 10p. Now share the 10p evenly i.e divide by 2, so the lesser one, the ball is 5p

[newmodarmy]

or just try £1 + 10p. no that doesn't work as the difference is only 90p.

So try £1.10 and £0, but that doesn't work either as the difference is £1.10,

So try somewhere in between: £1.05 and 5p- and that works as it's a £1 difference

[elliemay1]

But you don't have to do trial and error if you just take away the £1 then divide by 2, it's a simple formula that works when you get more difficult problems of that type

[newmodarmy]

Obviously that's how I'd do it too- but if you don't see it you don't see it.  It's a well known puzzle that catches a lot of people out

[elliemay1]

For example,a book and a pen cost £7.50, the book costs £2 more than the pen, how much does each cost?

Take away the £2, then divide by 2 which will give you the pen . Now add on the £2 to get the book price. Finally add the 2 together to check that your answer is correct

[newmodarmy]

Another simple one that's only simple if you see it and catches many people out. A car travels one mile up a hill at 30mph. How fast does it have to drive the 1 mile down the other side of the hill to make its average speed 60mph?

[Khandro]

I think elliemay's at 11.23 is an elegant explanation. Thank you all though. 

I took it from a review of a book on philosophy. Such a question seems to be attached to 'dual-process theory'.

'Such theories are well placed to explain simple errors of reasoning, which subjects readily recognise as such once they are pointed out.' 

[newmodarmy]

Is that a similar thought process to what happens when you ask "what do cows drink?" and a common immediate answer is milk?

[barry1010]

I understood this one straight away

[sandyRoe]

The car on the hill, 90 mph?

[newmodarmy]

No, that's not the answer, sandy

[Old_Geezer]

Surely this one is too blatant to puzzle folk. Subtract the 100p and divide the remainder by 2.

[THECORBYLOON]

If I can change the car question to make it easier to explain, say the journey one way was thirty mile, travelling at 30 mph would mean it took an hour.

To average 60mph there and back, it would need to travel sixty mile in an hour but it has already taken an hour to travel the first thirty mile of the journey so the desired average is not possible.

[JJ109]

newmodarmy - it is impossible

The car has taken 2 minutes to go up the hill 1 mile

At an average speed of 60 mph, the 2 miles up and down can only take 2 minutes, therefore as it has already taken 2 minutes to go up the hill, there is no time left to "go down"