Tejinder: What is your age, Mother?”
Mother: ” Well, Tejinder, our three ages add up to exactly seventy years.”
Tejinder: “Oh, 70! That is some figure. Father, what is your age? ”
Father: “Six times yours son.”
Tejinder: “Could I ever be half as old as you, Father?”
Father: “Yes, Tejinder; and at that time, our three ages will add up to exactly twice as much as to-day.”
Tejinder: “Oh, I will have to use bring a pen and paper to figure this out”.
Was Tejinder able to find the exact ages of everyone? If so, what are these ages?

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Age of the Mother: 29 years 2 months Age of the Father: 35 years Tejinder’s age: 5 years 10 months. Add them up: it comes to 70. Further check: Father’s age is 6 times the age of Tejinder After 23 years 4 months, the sum of their ages will amount to 140 years, double of what it is now.

Equations to solve the puzzle: Tejinder’s present age: T Mother’s present age: M Father’s present age: F

From the first clue: T + M + F = 70………………………… (1)

Second clue: father is six times the age of the son F = 6 x T………………………………… (2)

Third clue: in Y years, father’s age will be twice that of Tejinder. F + Y = 2 x (T + Y)……………………… (3)

Also then, the sum of times will be double the present sum: (T + Y) + (M + Y) + (F + Y) = 140 T + M + P + 3Y = 140 …………………….(4)

From (4) and (1) 3Y = 70 Y = 70/3 …………………………………….. (5)

Using (2) and (5) in (3) we have F + 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: F = 6 x T F = 6 x (70/12) F = 70/2

And using the values for T and P in (1) we have: T + M + F = 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 the respective ages are: Tejinder = 70/12 = 5.83333 = 5 years 10 months. Father = 70/2 = 35 = 35 years. Mother = 350/12 = 29.1666 = 29 years 2 months.


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