A Bat and a ball

Take cost of ball to be x -1 , and the cost of the bat to be x

x + (x - 1) = 1.10

2x - 1 = 1.10

2x = 2.10

x = $\frac{2.10}{2}$

x = $\boxed{1.05}$

Most people will think quickly and put ten pence because they subtract $1 from $1.10 which gives you 10p.The answer is 5p because if the ball is 5p the bat will be $1.05 which is $1 more than 5p.

Cost of (bat + ball = 1.10 $)

Cost of ( bat - ball = 1 $)

Add them :
                2 bat=2.10$

Therefore : cost of bat = 1.05 $

This question is there in Daniel Kanheman's book "Thinking Fast and Slow" which shows that human mind is actually two systems...one fast and the other slow. Our mind has the tendency to do least work and hence we intuitively answer this question $1 for the bat while 10p for the ball....which is not the case!!!

Let the pat=X

and the ball=Y

then : X+Y=1.10

X-Y=1

add the 2 equations

then : 2X=2.10

then X=1.05

bat=1.05

Let the cost of bat be x

So, cost of ball=x-1

x+x-1=1.10,

2x=2.10,

x=1.05.

Let the cost of the ball be x, and since the bat costs $1 more its cost is (x+1). The sum of all the goods is (2x + 1) = 1.1 so we subtract 1 for 2x = 0.1, then divide by 2 and get x=0.05. The cost of the bat is (x+1) = 0.05 + 1 = $1.05

take cost of ball as x; now bat = x+10; therefore x+x+10 = 1.10 2x = 0.10 => x=0.05 cost of ball = 0.05 $ cost of bat = 0.05 +1.0 = 1.05 $