Aptitude Day 21

Answer of Day 20: 16 years.

Problem on Ages 

Today we're gonna see another 3 problems...

1. The ratio of Kevin's age to Sana's age is 7:3. The product of their ages is 756. The ratio of their ages after 6 years will be:

Solution:
               Let their ages be 7x and 3x respectively.
               The product of their ages (7x)(3x) = 756
                                                              21x²= 756
                                                                  x²= 756/21 = 36
                                                                  x = 6
                The ratio of their ages after 6 years will be (7x+6) : (3x+6)
                                                                                            48: 24
                                                                                              2: 1
                                                   
 2. The present ages of three persons are in the proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages in years. 

Solution:
               Let their present ages be 4x, 7x and 9x respectively.
               Eight years ago, the sum of their ages = (4x-8) + (7x-8) + (9x-8) = 56
                                                                                                    20x-24 = 56
                                                                                                           20x = 80
                                                                                                               x = 4

               Their present ages are 4(4) = 16 years, 7(4) = 28 years and 9(4)= 36 years respectively.

3. The ratio of the ages of a man and his wife is 4:3. After 4 years, this ratio will be 9:7. If at the time of marriage, the ratio was 5:3, then how many years ago were they married?

Solution:
               Let their ages are 4x and 3x respectively.
               After 4 years, the ratio will be 9:7
               So, (4x+4)/(3x+4) = 9/7
                               7(4x+4) =  9(3x+4)
                                28x+28 = 27x+36
                                          x = 8
              Their ages are 32 and 24 years respectively.

              At the time of marriage, the ratio was 5:3
              They were married 'a' years ago.

              Hence, (32-a)/(24-a) = 5/3
                           3(32-a) = 5(24-a)
                                 96-3a = 120-5a
                                       2a = 24
                                         a = 12 years.