Problems On Ages

Details

We know, Shankar's age = Shanti's age + 22 ....(1)
Shankar's age = 72%(Shanti's age + Shankar's age)
Shankar's age = (72/100)Shanti's age + (72/100)Shankar's age
Shankar's age - (72/100)Shankar's age = (72/100)Shanti's age
(28/100)Shankar's age = (72/100)Shanti's age
Shankar's age = (18/7)Shanti's age ....(2)
Sub (2) in (1),
(18/7)Shanti's age = Shanti's age + 22
(18/7)Shanti's age - Shanti's age = 22
(11/7)Shanti's age = 22
Shanti's age = 14 yrs
Shanti's age 15 yrs hence = 14 + 15 = 29 yrs.

⇒ 3 years ago, the ratio of age of A and B = 5: 4 (5x, 4x)
⇒ The present age of A and B = 5x + 3, 4x + 3
⇒ Present age of C = Present age of A - 8
⇒ Present age of D = 12 - 7 = 5
⇒ Present age of C = 4 × present age of D
⇒ 4×5 = 20 years
⇒ Present age of A = 20 + 8 = 28 years
⇒ 5x + 3 = 28
⇒ 5x = 25
⇒ X = 5
⇒ The present age of B = 4x + 3 = 23 years

Details

⇒ Let current ages of Neesha and Brahma are X and Y
Given that
⇒ (X : Y) = (9:10) or (X/ Y) = (9/ 10) → X = (9Y/10)…… (a)
⇒ Ten years ago their ratios
⇒ (X-10: Y-10) = (4:5) o r (X-10/Y-10) = (4/5) …. (b)
⇒ By putting the value of X from (a) into (b)
⇒ ([(9y/10)-10]/y-10) = (4/5)
⇒ ((9y/2) -50) = 4y-40
⇒ (9y/2)-4y = -40+50
⇒ ((9y-8y)/2) = 10
⇒ we get Y = 20
⇒ Hence Brahma's present age is 20 yr.

Let the present age of Deccan be 'x' years and the present age of Vikram be 'y' years.
15 years ago, ratio of their ages = 2 : 1
(x - 15)/(y - 15) = 2/1
x - 15 = 2y - 30
x - 2y = -15 ...(i)
Given that their ages difference 5 years ago was 10 years. So, age difference between them will be same.
x - y = 10 ...(ii)
By solving the equation (i) and (ii),
x = 35 yrs; y = 25 yrs
15 years hence,
Age of Deccan = 35 + 15 = 50 yrs
Age of Vikram = 25 + 15 = 40 yrs
Ratio of their ages after 15 yrs = 50 : 40 = 5 : 4.

Given Total number of days in the month = 30
As the month begin with monday, so there will be five mondays in the month.
Then, Number of days in the month excluding Sundays = 30 - 5 = 25
Now, Average number of visitors in the month = [(visitors on Sundays × no. of mondays) + (visitors on other days × no. of days excluding mondays)]/Total number of days in the month
= [(510 × 5) + (240 × 25)]/30
= [2550 + 6000]/30
= 8550/30
= 285

$${\text{Ajit's father's age}}$$
$${\text{ = 50 years, }}$$
$${\text{Ajit's age}}$$
$${\text{ = }}\left( {\frac{3}{5} \times 50} \right){\text{years}}$$
$${\text{ = 30 years}}$$
$${\text{Ajit's wife's age}}$$
$${\text{ = }}\left( {\frac{4}{5} \times 30} \right){\text{years}}$$
$${\text{ = 24 years}}$$
$${\text{Ajit's son's age}}$$
$${\text{ = }}\left( {\frac{1}{3} \times 24} \right){\text{years}}$$
$${\text{ = 8 years}}$$

Let the present ages of the father and the daughter be f and s respectively.
F = 3s - 20
s = (f + 20)/3
As s is an integer, so f + 20 is divisible by 3.
Going by the choices it must be 55 years.

Sanjay’s age today = 17 decades,
Hence, 5 decades back, he must be 12 years old.
Suraj must be 36 years old, Because (3×12).
5 years back Suraj must be 41 years old today. Because (36+5).