My local bus company has recently expanded and no longer has enough room inside its garage for all of its buses.
Twelve of their buses have to be stored outside.
If they decide to increase their garage space by 40% they will have enough room for all of their current buses, plus enough room to store another twelve in the future.
Hint
Think about the 40%, and how many buses that represents.
Answer
72 buses.
Reasoning
The garage is currently full, with 12 more buses outside.
If we increase the garage space by 40%, there will be enough space to house those 12 buses, plus 12 more in the future, a total of 24 buses.
This means that 40% of the current garage capacity is 24 buses.
Therefore, 10% of the current garage capacity is 6 buses.
Therefore, 100% of the current garage capacity is 60 buses.
So, the current garage holds 60 buses, and there are 12 more outside.
Therefore, we have a total of 72 buses.
Double-Checking
They currently have 72 buses, 12 of which are outside, so 60 are inside.
Increasing the garage space of 60 buses by 40% will give room for 60 x 1.4 = 84 buses.
Which is the 72 they currently own, with space for 12 more buses in the future.
This confirms the answer.
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Puzzle 2
Tommy: "How old are you, mamma?"
Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."
Tommy: "That's a lot, isn't it? And how old are you, papa?"
Papa: "Just six times as old as you, my son."
Tommy: "Shall I ever be half as old as you, papa?"
Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."
Tommy: "And supposing I was born before you, papa; and supposing mamma had forgot all about it, and hadn't been at home when I came; and supposing--"
Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."
Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of mamma?
Mamma's Age, Amusements In Mathematics, Henry Ernest Dudeney.
Hint
The answer isn't a whole number of years, and algebra might be required.
Answer
29 years 2 months.
Reasoning #1
This answer is taken directly from the original book.
The age of Mamma must have been 29 years 2 months; that of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father.
Reasoning #2
Here's my answer, with a little algebra.
If we call Tommy T, Mamma M and Papa P we can see that:
"our three ages add up to exactly seventy years" gives us:
(1) T + M + P = 70
"Just six times as old as you" gives us:
(2) P = 6 x T
In an unknown number of years (Y) "Shall I ever be half as old as you" gives us:
(3) P + Y = 2 x (T + Y)
and "our three ages will add up to exactly twice as much as today" gives us:
(T + Y) + (M + Y) + (P + Y) = 140
which can be written as
(4) T + M + P + 3Y = 140
We can see from (4) and (1) that
3Y = 70
so
(5) Y = 70 ÷ 3
Using (2) and (5) in (3) we have
P + Y = 2 x (T + Y)
6 x T + 70 ÷ 3 = 2 x (T + 70 ÷ 3)
4 x T = 70 ÷ 3
(6) T = 70 ÷ 12
We can now use (6) in (2) to see that:
P = 6 x T
P = 6 x 70 ÷ 12
P = 70 ÷ 2
And using the values for T and P in (1) we have:
T + M + P = 70
70 ÷ 12 + M + 70 ÷ 2 = 70
Multiply throughout by 12 to give:
70 + 12 x M + 420 = 840
12 x M = 840 − 420 − 70
12 x M = 350
M = 350 ÷ 12
So:
Tommy = 70 ÷ 12 = 5.83333 = 5 years 10 months. Papa = 70 ÷ 2 = 35 = 35 years. Mamma = 350 ÷ 12 = 29.1666 = 29 years 2 months.
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Puzzle 3
Which is larger:
square inches in a piece of carpet 15 yards by 5 yardsfeet in a 20-mile walk
Hint
One of the words is waterfall (wat + erf + all).
Answers
som + eth + ing = something
hai + rbr + ush = hairbrush
gra + ssl + and = grassland
pin + eap + ple = pineapple
pol + ice + man = policeman
mea + nwh + ile = meanwhile
wat + erf + all = waterfall
sca + rec + row = scarecrow
yes + ter + day = yesterday
obs + tin + ate = obstinate
