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Grand Father, Father and Grand Son

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Number Puzzle #69

One Grand Father, One Father and One Grand Son.
Sum of their age is 140 Years.
Grand Son’s age in month is equal to Grand Father’s age in years.
Grand Son’s age in days is equal to Father’s age in weeks.
What is the Age of all three?
–In Hindi–
Ek Dada Ek Baap Ek Pota 3no Ki Total Age 140 Years Hai Pota jitne Month Ka Dada utne Saal ka Pota jinte din ka Baap utne week ka hai Batao 3no Kitne kinte Saal k Hain?


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Answer: Son’s age: 7 Years, Father Age: 49 Years and Grand Father’s Age: 84 Years.

Lets assume the age(in years) of Grand Father, Father and Son as GF, F and S respectively.
Sum of their age is 140 Years
=> Equation 1 => GF + F + S = 140
Grand Son’s age in month = Grand Father’s age in years
S*12 = GF => Equation 2=> GF = 12S
Grand Son’s age in days = Father’s age in weeks
S*365 = F*(365/7)
S = F/7 => Equation 3 => F = 7S

Now we have three variables and three equations, we can easily solve it
12S + 7S + S = 140
20s= 140 => S = 7
F = 7S = 49
GF = 12S = 84.

Number Puzzle #68, 1, 10, 30, ?, 130

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Number Puzzle #68

missing number in 1, 10, 30, ??, 130

missing number in 1, 10, 30, ??, 130

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Actually this is a GP with first element as 1 and variable factor. where the factor comes from this series
1, 3, 7, 13.

Tn = Tn-1 + 2^(n-1);
T1 = 1;
T2 = T1 + 2^(2-1)= 1 + 2 = 3;
T3 = T2 + 2^(3-1) = 3 + 4 = 7;
T4 = T3 + 2^(4-1) = 7 + 6 = 13

nth number in GP = first number * (10)(Tn-1 in series);
First Element in GP = 1;
Second Element in GP(i.e. n = 2) = 1*10*(T1 in series); = 10
Third element in GP(i.e. n =3) = 1*10*(T2 in series) = 1*10*3 = 30
Fourth element in GP (i.e. n =4) = 1*10*(T3 in series) = 1*10*7 = 70
Fifth element in GP (i.e. n =5) = 1*10*(T4 in series) = 1*10*13 = 130

Thus the missing number here is 70.

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