Let the present age of the son be x and that of the father be 4x years.
? (x - 5) + (4x - 5) = 60
? 5x = 70
? x = 14 years
? Father's present age = 4x = 56 years
Let the mother's age 2 years ago be 4x and daughter's age 2 years ago be be x.
? (4x + 8) - (x + 8) = 12
? 3x = 12
? x = 4
? Mother's present age = 4x + 2 = 18 years
and daughter's present age = x + 2 = 6 years
? Required ratio = 3 : 1
Let the average age of A, B and C be N years.
? Total age of A, B and C = 3 x N = 3N years
Now, according to the question,
? 3N - (2N + N/2) = 5
? N = 10 years.
Let the present age of father be x years and the sum of present ages of 2 sons be y years.
? x = 3y ...(i)
? (x + 20) = (y + 20 + 20) ...(ii) [20 will be added twice as for 2 children]
Solving (i) and (ii), we get
x = 30 years
Let son's present age be x years and father's age = (45 - x) years.
? (x - 5) (45 - x - 5) = 4 ( 45 - x - 5)
? (40 - x) (x - 9) = 0
? x = 9years
? The son's age = 9 years
Father's age = 45 - 9 = 36 years
? Anup's age = (5 - 2) years = 3 years
Let Randheer's age be x years.
Then, (x - 6)/18 = 3
? x = 54 + 6 = 60
Age of C < Age of A < Age of B
From question,
A = C + x ....(i)
B = A + x ....(ii)
From equation (i) and (ii)
A - B = C - A
? 2A = B + C
? A = (B + C) / 2
Given that sum of the ages of B and C is 40 years.
So, A = (B + C) / 2 = 40/2 = 20 Years
Let the present age of A is x and present age of B is y.
Therefore, x + y = 63 ....(i)
Difference of their ages is = (x - y) years.
When A was as old as B then, A's age was 'y; years and B's age was [y - (x - y)] = (2y - x) years.
Given that present age of A is twice the past age of B.
? x = 2(2y - x)
? 3x = 4y .....(ii)
From (i) and (ii)
x = 36 and y = 27
So the difference in age of A and B is 36 - 27 = 9 years.
Let A's age = x years and B's age = y years
As per the first condition,
? (x + 15) = 2(y + 15)
? x - 2 y = 15 ....(i)
As the per second condition,
? (x - 5) = 4(y - 5)
? x - 4 y = -15 ....(ii)
Solving (i) and (ii) one get's, x = 45, y = 15
? A's age = 45 years
B's age = 15 years
? Difference of their ages = 45 - 15 = 30 years
? S / F = 1 / 5
? F = 5 S, .....(i)
? M / F = 4 / 5
? M = 4 / 5 F ....(ii)
? (S + 2) / (M + 2) = 3 / 10
? 10S + 20 = 3M + 6 ....(iii)
From (i), (ii) and (iii)
? (12 - 10)S = 20 - 6
? 2S = 14
? S = 7 years
? F = 5S = 5 x 7 = 35 years.
Let the ages of Harish and Seema be x and y respectively.
According to the question,
xy = 240 ....(i)
2y - x = 4 ....(ii)
Solving equations (i) and (ii), we get
y = 12 years
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