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?
Click here to learn more
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.
