Aptitude Problems on Ages Solved examples

1.The sum of the ages of a mother and daughter is 50 years. Also 5 years ago, mother's age was 7 times the age of the daughter. The percentages of the mother and daughter respectively are:
Explanation:
Let the daughter's present age be x years.
then, mother's present age = (50-x) years
Now, 7(x-5) = (50-x-5)
     7x-35 = 45-x
           8x = 80
             x = 10
So, The Present ages are 40 yrs and 10 yrs.

2. Puspha is twice  as old as Rita was two years ago. If the difference between their ages be 2 years, how old is pushpa today?
Explanation:
Let Rita's age 2 years ago be x years.
Pushpa's present age = (2x) years
2x-(x+2) = 2
        x-2 = 2
            x = 4

3. The Ratio of Laxmi's age to the age of her mother is 3:11. The Difference of their ages is 24 years. The ratio of their ages after 3 years will be:
Explanation:
11x - 3x = 24
         8x = 24
          x = 24/8
          x = 3
Ratio of their ages after 3 years
 = (3x+3) : (11x+3)
 = 12 : 36
 = 1 : 3

4. 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?
Explanation:
Let A's age 10 yrs ago = x yrs
Then, B's age 10yrs ago = 2x yrs
=> x + 10/ 2x + 10 = 3/4
=> 4(x + 10) = 3(2x + 10)
=> x = 5
Total of their Present ages = (x + 10 + 2x + 10)
                                        = 3x + 20
                                        = 3(5) + 20
                                        = 35

5. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
=> (2x + 2) + 2x + x = 27
=> 5x = 25
=>   x = 5.
Hence, B's age = 2x
                        = 10 years.