SOLUTION: The Sum of the ages of A and B is 42 years. 3 years back, the age of A was 5 times the age of B. Find the difference between the present ages of A and B.

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Question 513603: The Sum of the ages of A and B is 42 years.
3 years back, the age of A was 5 times the age of B. Find the difference between the present ages of A and B.

Answer by Maths68(1474) About Me  (Show Source):
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Let
Present age of A = a
Present age of B = b


The Sum of the ages of A and B is 42 years.
a+b=42
a=42-b..........(1)
3 years back
a-3=b-3
then
the age of A was 5 times the age of B
a-3=5(b-3)
a-3=5b-15
a=5b-15+3
a=5b-12.............(2)
Subtitue the value of a in (2) from (1)
42-b=5b-12
-b-5b=-12-42
-6b=-54
-6b/-6=-54/-6
b=9
Put the value of b in (1)
a=42-9
a=33
Present age of A = a = 33 years old
Present age of B = b = 9 years old
Three years bakc B was = 9-3 = 6
Three years bakc A was = 33-3 = 30 (which is 5 times of 6)