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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.

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