Solving problems on ages is a two step process.
Create linear equations based on statements provided.
Solve the equations to get the values as required ages.
Solved Examples
Q 1 - If the ratio of ages of two persons Ram and sham is 5:4 . After Three years their age ratio changes and becomes 11:9. In that case tell about the present age of mr. sham.
Answer - B
Explanation
If the age of Mr. Ram 5x and 4x is the age of Mr. sham. Then, ( 5x+3) /( 4x+3) = 11/9 ⇒ 9 (5x+3)= 11 (4x+3) ⇒ x= (33-27) = 6 So the present age of Mr. sham = 6*4 = 24 years.
Q 2 - A mother is 30 time older in the comparison of her daughter. After the period of 18 year , the mother age would be thrice in the comparison of his daughter . In that case tell about the present age of mother.
Answer - A
Explanation
Let daughter present age be x year . in that case mother present age would be = 30x years 30x+ 18 = 3 (x+ 18) ⇒ 27x = 36 ⇒ x = 4/3 ∴ so the present age of mother = (30* 4/3) = 40 years.
Q 3 - The ratio of present ages of three persons ajay , vijay and sanjay are in the proportion of 4: 7: 9. Before 8 year total sum of their age is 56. What should be the present ages?
Answer - A
Explanation
If the present age of ajay , vijay and sanjay is 4x , 7x and 9x years. Total sum of ages of ajay, vijay and sanjay before 8 years ago = (4x-8)+(7x-8)+(9x-8) =(20x-24) years. ∴ 20x-24 = 56 ⇒ 20x = 80 ⇒ x= 4 Hence, it proves that age of ajay is 4*4 = 16 years, vijay (7*4) = 28 years and sanjay (9* 4) = 36 years.
Q 4 - Daughter's present age is 2/5 in the comparison of her mother .8 year later , age of her daughter will be 1/2 in the comparison of her mother. Find out mother present age?
Answer - B
Explanation
If the present age of mother is equal to x year. In that situation the daughter present age would be = 2x/5 years. 2x/5 + 8 = 1/2 (x+8) ⇒ 4x+ 80 = 5x+40 ⇒ x = 40. The mother age at the present time is = 40 years.
Q 5 - Ajay age was double in the comparison of bhuvan before 3 years. Seven years hence, the sum of both ages would be 83 years. What should be the age at the present time of both?
Answer - C
Explanation
Before 3 year let bhuvan age be x years. 3 years before , ajay age will be 2x years. Now Bhuwan's age =(x+3) years and ajay age = (2x+3) years. (x+3)+7+(2x+3)+7 = 83 ⇒ 3x+20 = 83 ⇒ 3x = 63 ⇒ x = 21 Now the bhuwan present age = (21+3) = 24 years Now the ajay present age = (2 *21+3) years = 45 years.
Q 6 - I am 4 year older in the comparison of my sister, but my brother who is the youngest among us is 7 year younger to myself. My father is three times in the comparison of my brother. The present age of my sister 18 year and my father is 3 year older in the comparison of my mother. In that situation what should be the present age of my mother?.
Answer - A
Explanation
If my sister age is x years. Then, Sister - x I - x+4 Brother - (x+4-7) = x-3 Father - 3 (x-3) Given x = 18 ∴ Father's age = 3(18-3) = 45 years. Mother age = (45-3) = 42 years.
Q 7 - Ajay is as much younger to vijay as he is older to vinay. If 48 years is the sum of the ages of vijay and buwan . Then find out the present age of Mr. ajay ?
Answer - D
Explanation
V-A = A- B ⇒ V+B = 2A =48 ⇒ 24 Now, We can say that the present age of Mr. Ajay is 24 years.
Q 8 - If 100 year is equal to the sum of the ages of father and son. 2:1 was the ratio of father and son before the period of 5 years. Find out the ratio of ages which would be after the period 10 year.
Answer - D
Explanation
If the age of father at the present time = x years His son age at the present time = (100-x) years. x-5 / (100-x-5) = 2/1 ⇒ (x-5) = 2(95-x) ⇒ 3x = 195 ⇒ x = 65 Ratio of the ages of man and son after 10 years = (65+10)/(35+10)= 75/45 = 5/3 = 5:3
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