I recently went to the shop and purchased 4 items.
Three of the items cost:
There was quite a long queue, and as I was quite bored, I was playing with my pocket calculator whilst waiting.
Very curiously, the 4 prices added to the same number as I got when I multiplied the 4 prices together.
What was the price of the 4th item?
[Ref: ZAPY] © Kevin Stone
Hint: What do the 3 numbers add and multiply to give so far?
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.
The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.
You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.
The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
8.50 + P = 18.00 x P
8.50 = 18.00 x P - P
8.50 = 17.00 x P
8.50 ÷ 17.00 = P
P = 0.50. QED.
A car travels at a speed of 64mph and its fuel consumption is 28 mpg.
It has a 11 gallon tank which was full when it started but at that very moment began to leak fuel.
After 112 miles the car stops with a completely empty tank.
How many gallons per hour was it losing?
[Ref: ZJAI] © Kevin Stone
Hint: How long did the journey take, and how much fuel did it use?
Answer: 4 gallons per hour.
Remember that Time = Distance ÷ Speed.
The car travels 112 miles, which uses 112 miles ÷ 28 mpg = 4 gallons of fuel. This leaves 7 gallons.
The car took 112 miles ÷ 64 mph = 1.75 hours (1 hour 45 mins) to travel the 112 miles, which means the 7 gallons were lost in 1 hour 45 mins.
Therefore the car was losing the fuel at a rate of 7 gallons ÷ 1.75 hours = 4 gallons per hour. QED.
What four digit number has digit 2 smaller than digit 4 which is two thirds of digit 1 which is two thirds of digit 3 which is three times digit 2?
[Ref: ZVLZ] © Kevin Stone
Digit3 can only be 3, 6 or 9 (as it's 3 x Digit2).
Digit2 can only be 1, 2 or 3.
Digit1 can only be 2, 4 or 6.
But, since Digit4 is two thirds of Digit1, Digit1 must be 6. Making Digit4 4 and making Digit3 9. Making Digit2 3.
Giving 6394. QED.
If you were to spell out the numbers in full, (One, Two, Three, etc), how far would you have to go until you found the letter 'A'?
Hint: Start counting now.
Unless you use British English when the answer becomes 101 = one hundred And one.
My local bus company has recently expanded and no longer has enough room for all of its buses.
Twelve of their buses have to be stored outside.
If they decide to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future.
How many buses does the company currently own?
[Ref: ZWOL] © Kevin Stone
Hint: A tricky puzzle that will need a little algebra (or clever thinking).
They have enough room for 60 of these, expanding the 60 capacity by 40% will give them enough room for 84, which we know is 12 more spaces than they currently need.
If they have B buses and S spaces before the expansion, they have enough room for:
S = B - 12 
After the expansion they have more spaces, and enough room for:
S + 0.4 x S = B + 12 
Rewriting  as:
1.4S = B + 12
and again as
B = 1.4S - 12 
We can rewrite  as:
B = S + 12 
Making  =  we have:
1.4S - 12 = S + 12
Subtracting S from both sides gives:
0.4S - 12 = 12
Adding 12 to both sides gives:
0.4S = 24
Multiplying by 10 and dividing by 4 on both sides gives:
S = 60
Using S = 60 in  gives B = 72. QED.