40,2 years ago a father was 6 times older than his son. After 18 years he will become double as old as his son. Find the present age
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Let :
- Present age of father = x years
- Present age of son = y years
Given :
- 2 years ago , father was 6 times older than his son
- After 18 years he will become double as old as his son
To find :
- Present age of father
- Present age of son
Solution :
2 years ago -
- Age of father = x-2
- Age of son = y-2
Also , Age of father = 6×Age of son
(x-2) = 6(y-2)
x-2 = 6y - 12
x = 6y - 12 + 2
x = 6y - 10 ....... equation 1
18 years later -
- Age of father = x+18
- Age of son = y+18
Also , Age of father = 2×(age of son)
(x+18) = 2×(y+18)
x + 18 = 2y + 36
x = 2y + 36 - 18
x = 2y + 18 .......... equation 2
Putting value of, x from equation 1 into equation 2,
we get;
6y - 10 = 2y + 18
6y - 2y = 18 + 10
4y = 28
y = 28 ÷ 4
y = 7
Putting value of y in equation 1, we get ;
x = 6(7) - 10
x = 42 - 10
x = 32
ANSWER :
- Present age of father = 32 years
- Present age of son = 7 years
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