Problems On Ages

Let son's present age = p years
Present age of father = (57 - p) years
(51-p-6) = 4(p-6)
51-p = 4p-24
p=15 years

Let the present age of Anitesh be 'x'.
At present, Anitesh is one-third the age of his father Rajesh.
So, present age of father = 3x
we know that,
3x - 5 = 4(x - 5)
3x - 5 = 4x - 20
x = 15 years
∴ present age of father = 3x = 3(15) = 45 years
So, father's age after 5 years = 45 + 5 = 50 years:

Given ratio of present ages of Ashok and Himesh = 3: 4
⇒ Present age of Ashok = 3x
and Present age of Himesh = 4x
Given, Pradeep is 6 years older than Ashok and two years younger than Himesh
⇒ Present age of Pradeep = Present ages of Ashok + 6 = Present age of Himesh - 2
⇒ Present age of Pradeep = 3x + 6 = 4x - 2
⇒ 3x + 6 = 4x - 2
⇒ 4x - 3x = 6 +2
⇒ x = 8
∴ Present age of Ashok = 3x = 3 x 8 = 24 years
Present age of Pradeep = Present ages of Ashok + 6 = 24 + 6 = 30 years
Now, Sum of the present ages of Ashok and Pradeep = 24 + 30 = 54 years

Let son's age be $$x$$ years.
Then, mother's age = (56 $$-\, x\,$$) years
$$\left( {56 - x} \right)+4 = 3\left( {x + 4} \right)$$
$$ ⇒ 60 - x = 3x + 12 $$
$$ ⇒ 4x = 48 $$
$$ ⇒ x = 12$$
∴ Daughter's age = 12 years
And the mother's age = (56 $$-$$ 12) = 44 years

Let the present ages of son and mother be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x - 30
⇒ 6x = 84
⇒ x = 14.
⇒ Daughter's age after 6 years = (x+ 6) = 20 years.

Let the son's present age be x years. Then, man's present age = (x + 24) years
⇒ (x + 24) + 2 = 2(x + 2)
⇒ x + 26 = 2x + 4
So, x = 22

We know Present ages of Rajesh and Varoun = 7 : 9
5 yrs ago, ratio of their ages = 3 : 4
Let the present age of Rajesh and Varoun be 7x and 9x respectively.
As per question,
(7x - 5)/(9x - 5) = $$\frac{3}{4}$$
28x - 20 = 27x - 15
x = 5
So, present age of Varoun = 9x = 9(5) = 45 yrs.
Varoun's age after 3 yearss = 45 + 3 = 48 yrs.

Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R - Q = ?.
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
∴ (R-Q) cannot be determined.

Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20
∴ Required ratio
= (3x + 10) : (x + 10)
= 70 : 30
= 7 : 3

Let the present age of the man be 'P' and son be 'Q',
Given, P + Q = 64 or Q = (64 - P)
Now the man says "I am five times as old as you were, when I was as old as you are",
So, P = 5[B - (P - Q)]
We get 6P = 10Q,
Substitute value for Q,
6P = 10(64 - P),
Therefore P = 40, Q = 24.