### Problems on Ages - 1

1. One year ago Jaya was four times as old as her daughter Nikitha.  Six years hence, Mrs.Jaya's age will exceed her daughter's age by 9 years. The ratio of the present ages of Jaya and her daughter is :
a. 9 : 2
b. 11: 3
c. 12: 5
d. 13: 4
Correct Option: D
Explanation:
Let Nikitha's age 1 year ago = x
Then Jaya's age 1 year ago = 4 x
After 6 years their ages are 4x+7, x+7
(4x+7)-(x+7)=9 or x = 3
Present age of Jaya = (12+1) years = 13 years
Present age of Nikitha = (3+1) years = 4 years
Ratio of their ages = 13 : 4

2. Five years ago, the total of the ages of a father and his son was 40 years. The ratio of their present ages is 4 : 1. What is the present age of the father ?
a. 30 years
b. 20 years
c. 25 years
d. None of these
Correct Option: D
Explanation:
Let son's age = x. Then father's age = 4x
(x-5)+(4x-5)=40 $\Rightarrow$ x = 10
Present age of father = 40 years

3. A father is twice as old as his son. 20 years ago the age of the father was 12 times the age of the son. The present age of the father is :
a. 44 years
b. 32 years
c. 22 years
d. 45 years
Correct Option: A
Explanation:
Let son's age = x. Then, father's age = 2x.
12(x-20)=(2x-20)$\Rightarrow$x=22
Father's present age = 44 years

4. The ratio of the ages of Jaya and Ravi is 2:5. After 8 years, their ages will be in the ratio of 1:2. The difference in their present ages is : ( in years )
a. 24
b. 26
c. 29
d. 32
Correct Option: A
Explanation:
Let Jaya's age = 2x or Ravi's age = 5x.
$\displaystyle\frac{{2x + 8}}{{5x + 8}} = \displaystyle\frac{1}{2} \Rightarrow 2(2x + 8)$= (5x+8)$\Rightarrow$ x = 8
Jaya's age = 16 years
Ravi's age = 40 years
Difference of their ages = 24 years

5. The ages of Ravi Rani are in the ratio of 3:5. After 9 years, the ratio of their ages will become 3:4. The present age of Rani is : (in years )
a. 9
b. 15
c. 18
d. 24
Correct Option: B
Explanation:
Let Ravi's age = 3x or Rani's age = 5x
$\displaystyle\frac{{3x + 9}}{{5x + 9}} = \displaystyle\frac{3}{4} \Rightarrow 4(3x + 9) = 3(5x + 9) \Rightarrow x = 3$
Rani's age = 15 years

6. The ratio of the ages of Meena and Meera is 4:3. The sum of their ages is 28 years. The ratio of their ages after 8 years will be :
a. 4:3
b. 12:11
c. 7:4
d. 6:5
Correct Option: D
Explanation:
Let Meena's age = 4x or Meera's age = 3x. Then,
4x+3x=28$\Rightarrow$ x = 4
Meena's age  = 16 years or Meera's age=12 years
After 8 years their ages are 24 and 20.  So ratio is 6 : 5

7. Ten years ago A was half of B in age. If the ratio of their present ages is 3:4 , what will be the total of their present ages ?
a. 8 years
b. 20 years
c. 35 years
d. 45 years
Correct Option: C
Explanation:
Let A's age 10 years ago = x years
Then B's age 10 years ago = 2x years
$\displaystyle\frac{{x + 10}}{{2x + 10}} = \displaystyle\frac{3}{4} \Rightarrow 4(x + 10)$ = 3(2x+10) $\Rightarrow$ x = 5
Total of heir present ages =(x+10+2x+10)=(3x+20)=35 years

8. The ratio of Vimal's age and Aruna's age is 3:5 and sum of their ages is 80 years. The ratio of their ages after 10 years will be :
a. 2 : 3
b. 1 : 2
c. 3 : 2
d. 3 : 5
Correct Option: A
Explanation:
3x+5x=80$\Rightarrow$x = 10
Ratio of their ages after 10 years =(3x+10 : 5x+10) = 40:60 = 2:3

Ramakrishna Salagrama