Problems On Ages

Three years ago, Neena was thrice as old as his sister Meena. After three years Neena will be twice as old as Meena. What is the present age of Meena:
Explanation :
P - 3 = 3 ×(R - 3) —(1)
P + 3 = 2 ×(R + 3) —(2)
Solving eqn (1) and (2) R = 9

Current ages of Akhilesh = 4A and Naveen = 3A
So that 4A + 6 = 26
A = 5
Current age of Naveen = 3A
⇒ 3×5 = 15 years

⇒ Let the son's present age be×years.
⇒ Then the father's present age is (x + 34) years.
⇒ Father's age after 10 years = (x + 44) years
⇒ Son's age after 10 years = (x + 10) years
⇒ (x + 44) = 3(x + 10)
⇒ x + 44 = 3x + 30
⇒ 2x = 14
⇒ x = 7

Let the present ages of Pradeep, Prasanna and Pratap be k, l and m respectively.
k/l = 5/x
k = m - 18
m + 9 = 47
k - l = m
⇒ m = 47 - 9 = 38 years
⇒ k = 38 -18 = 20 years
⇒ 20/l = 5/x ⇒ l = 4x
⇒ 4x - 20 = 38
⇒ 4x = 58 ⇒ x = 14.5

Let, father’s current age is A years.
Then, Man’s current age = $$\frac{2}{5}×\text{A}$$years.

 $$\frac{2}{5}×\text{A}$$+8=$$\frac{1}{2}\text{A}+{8}$$

2(2A+40) = 5(A+8)

A = 40

Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x = 80
⇒ x = 4
∴ Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

Mother's age when Monisha's brother was born = 36 years.
Father's age when Monisha's brother was born = (38 + 4) years = 42 years.
∴ Required difference = (42 - 36) years = 6 years.

$${\text{Let}}\,{\text{the}}\,{\text{mother's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}{\text{.}}$$
$${\text{Then,}}\,{\text{the}}\,{\text{person's}}\,{\text{present}}\,{\text{age}}$$
$$ = {\frac{2}{5}x} \,\,{\text{years}}$$
$$\therefore {\frac{2}{5}x + 8} = \frac{1}{2}\left( {x + 8} \right)$$
$$ ⇒ 2\left( {2x + 40} \right) = 5\left( {x + 8} \right)$$
$$ ⇒ x = 40$$

Let Indu's age be 7x years.
Then, Darsha's age = 3x years
$$\therefore \frac{{7x + 6}}{{3x + 6}} = \frac{5}{3}$$
$$ ⇒ 3\left( {7x + 6} \right) = 5\left( {3x + 6} \right)$$
$$ ⇒ 21x + 18 = 15x + 30$$
$$ ⇒ 6x + 12$$
$$ ⇒ x = 2$$
Difference in their ages = (7x - 3x) years
= 4x years
= (4 × 2) years
= 8 years

Let A's age be 5x years.
Then, B's age = 6x years
$$\therefore \frac{{5x + 6}}{{6x + 6}} = \frac{6}{7}$$
$$ ⇒ 7\left( {5x + 6} \right) = 6\left( {6x + 6} \right)$$
$$ ⇒ 35x + 42 = 36x + 36$$
$$ ⇒ x = 6$$
B's age 5 years ago = (6x - 5) years
= (6 × 6 - 5) years
= 31 years