Question 515621: Five years ago. A's age was four times B's age, 6 years hence A's age to B's is 5:2. Find the ages of A and B at present. Answer by Maths68(1474) (Show Source):
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Present age of A = a
Present age of B = b
Five years ago
a-5=b-5
Then
A was 4 time of B's age
a-5=4(b-5)
a-5=4b-20
a=4b-20+5
a=4b-15..............(1)
In 6 years
A will be = a+6
B will be = b+6
Then
A's age to B's is 5:2
a+6 / b+6 = 5/2
2(a+6)=5(b+6)
2a+12=5b+30
2a=5b+30-12
2a=5b+18
2a=5b+18..........(2)
Put the value of a in (2) from (1)
2(4b-15)=5b+18
8b-30=5b+18
8b-5b=18+30
3b=48
3b/3=48/3
b=16
Put the value of b in (1)
a=4b-15
a=4(16)-15
a=64-15
a=49
Present age of A = a = 49 years old
Present age of B = b = 16 years old
Five years ago B was = 16-5 = 11
Five years ago A was = 49-5 = 44 (which is 4 times of 11)
In six years there ages will be in ratio = 49+6 / 16+6 = 55/22=5/2
