[OK]

See Details
Privacy Policy + T&C

We use cookies to personalise content and adverts. We also share information about your use of our site with our advertising partners who may combine it with other information you’ve provided to them or they’ve collected from your use of their services. You also agree to our terms and conditions (T&C).

BB Logo
Spacer
Line
Line

Puzzle - Answer

Puzzle ImageTommy: "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?

 [Ref: ZPYU] Mamma's Age. Amusements In Mathematics by Henry Ernest Dudeney (1917).

Answer: 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.

The answer above is taken from the original book, here is another version of the answer:

If we call Tommy T, Mamma M and Papa P we can see that:

"our three ages add up to exactly seventy years" leads to

   T + M + P = 70 (1)

"Just six times as old as you" leads to

   P = 6 x T (2)

In an unknown number of years (Y) "Shall I ever be half as old as you" leads to:

   P + Y = 2 x (T + Y) (3)

and "our three ages will add up to exactly twice as much as to-day" leads to:

   (T + Y) + (M + Y) + (P + Y) = 140

which can be written as

   T + M + P + 3Y = 140 (4)

We can see from (4) and (1) that

   3Y = 70

so

   Y = 70 ÷ 3   (5)

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

              T = 70÷12 (6)

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.

QED.

Back to the puzzles...


Our Favourite Illusions

 Shadow Illusion

 What Am I?

 Hidden Faces

 Impossible Waterfall?

 Same Eyes?

 Impossible Prongs?

 Duck Or Rabbit?

 Spinning Dancer

 Who Turned To?

 Blind Spot

 The Butterfly

 Parallel Cafe Wall Lines?

 

 



BrainBashers™ is a trademark. We use cookies to personalise content and adverts. We also share information about your use of our site with our advertising partners who may combine it with other information you’ve provided to them or they’ve collected from your use of their services. For more information please view our privacy policy. By using the site you also agree to our terms and conditions.

[Added September 1997]

Line
Line