Maths Puzzles

Puzzle 1

A fire engine was rushing to a small fire, 15 miles away.
The fire engine set out with 120 gallons of water, however, the water tank had a leak and the fire engine was losing water at the rate of 2 gallons per minute.
The fire engine travelled at a constant 30 miles per hour.
The fire required 50 gallons of water - did the fire engine have enough water when it arrived?

[Ref: ZQQW] © Kevin Stone

Hint: How long did the journey take?

Answer: Yes.
The journey took 30 minutes.
In that time the fire engine lost 60 gallons of water - leaving 60 gallons with which to fight the fire.

Puzzle 2

Alan's son Daniel, is exactly one fifth of Alan's age.
In 21 years time, Alan will be exactly twice Daniel's age.
Betty's is exactly seven times the age of her daughter, Jessica.
In 8 years time, Betty will be three times the age of Jessica.
How old are Daniel and Jessica now?

[Ref: ZQZZ] © Kevin Stone

Hint: A little bit of algebra might help.

Answer: Daniel is 7 years old and Jessica is 4 years old.
The first half of the question involves Daniel (D) and Alan (A).
Daniel is currently one fifth of Alan's age, so:
A = D x 5 (1)
In 21 years time, Alan will be twice his age, so:
A + 21 = (D + 21) x 2 (2)
Using (1) in (2) gives:
A + 21 = (D + 21) x 2
5D + 21 = (D + 21) x 2
5D + 21 = 2D + 42
3D = 21
D = 7
So Daniel is 7 (and Alan is 35).
The second half of the question involves Jessica (J) and Betty (B).
Betty's is exactly seven times the age of Jessica:
B = J x 7 (3)
In 8 years time, Betty will be three times the age of Jessica, so:
B + 8 = (J + 8) x 3 (4)
Using (3) in (4) gives:
B + 8 = (J + 8) x 3
7J + 8 = (J + 8) x 3
7J + 8 = 3J + 24
4J = 16
J = 4
So Jessica is 4 (and Betty is 28). QED.

Puzzle 3

Complete this grid with the digits 1 to 6 to make the sum correct.
Perform each mathematical operation in the order shown, from left to right, e.g. 1 + 2 x 3 is treated as (1 + 2) x 3 = 9.
Note: there is no ÷ 1, and at no point is a decimal or fraction used.

[Ref: ZXLN] © Kevin Stone

Hint: The first number is 2.

Answer:

Puzzle 4

Within the BrainBashers school, the science department has three disciplines.
In total, 280 students study chemistry, 254 students study physics and 280 students study biology.
97 students study both chemistry and physics, 138 students study both physics and biology, 152 students study both chemistry and biology.
73 students study all three disciplines.
Can you determine how many students there are in the science department? The answer is well below 814.

[Ref: ZZYU] © Kevin Stone

Hint: How many students study chemistry and physics, but not biology?

Answer: 500 students.

The answer is most easily seen if three intersecting circles are drawn, and the numbers inside each section worked out.

Puzzle 5

What value of * makes the following correct:

[Ref: ZWPF] © Kevin Stone

Hint: The answer is a whole number less than 10.

Answer: 3.

Checking that 3 works:

3 3 3 3
- - - + - = -
3 2 4 12
1 - 1.5 + 0.75 = 0.25
0.25 = 0.25, which confirms that 3 is correct.
To deduce the answer directly from the question, we can multiply throughout by 12,
* * * *
- - - + - = -
* 2 4 12
to give:
12 - 6* + 3* = 1*
12 - 3* = 1*
12 = 4*
3 = *
As required.