Aptitude Day 17

Problem On Ages

                 Today, we're gonna see another 3 problems regarding this topic.

1. The product of the ages of A and B is 240. If twice the age of B is more than A's age by 4 years, what's B's age?

Solution:  AB= 240
                 B=240/A
                 2B=A+4

                 2(240/A)=A+4

                 (480/A)-A=4  

                 480-A² =4A

                 A²+4A-480=0

                 (A+24)(A-20)=0

                  A=20

                  B=240/A

                  B=240/20

                  B=12

Hence, B is 12 years old.

2. One year ago, the ratio of  A and B was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is B?

  

Solution: (6x+1)+4= 6x+5

                (7x+1)+4=7x+5

               (6x+5)/(7x+5) = 7/8

               8(6x+5)= 7(7x+5)

               48x+40=49x+35

                      x=5

B's age = 7x+1

            = 7(5)+1

            = 36 

Hence, B's present age is 36 years.

3. Varun's age after 6 years will be three-seventh of his mother's age. Ten years ago, the ratio of their ages was 1:5. What's Varun's mother's age at present?

Solution: (x+10)+6 = x+16

                (5x+10)+6 = 5x+16

                x+16 = 3/7 (5x+16)

                7x+112 = 15x+48

                     8x=64

                       x=8.

Mother's age is 5x+10= 50 years.