two years ago,the age of a father was three and a half times the age of his daughter then.six years hence,the age of father will be ten years more than twice the age of his daughter then.find their present ages.
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The present age of the father is 44 years and present age of daughter is 14 years.
Step-by-step explanation:
Let the present age of father be “x” years and the present age of daughter be “y” years.
For equation 1: Ages of father and daughter 2 years ago
According to the question,
[x-2] = 3 ½ * [y-2]
⇒ [x-2] = (7/2)[y-2]
⇒ 2x – 4 = 7y -14
⇒ 2x – 7y + 10 = 0 ……. (i)
For equation 2: Ages of father and daughter 6 years hence
According to the question,
[x+6] = 10 + 2[y+6]
⇒ x + 6 = 10 + 2y + 12
⇒ x – 2y – 16 = 0 ……. (ii)
On multiplying 2 throughout the eq. (ii) and then subtracting the eq. (i) from (ii), we get
2x – 4y – 32 = 0
2x – 7y + 10 = 0
- + -
------------------------
3y = 42
-----------------------
∴ y = 14 years
Now, substituting the value of y = 14 in eq. (ii), we get
x – (2*14) – 16 = 0
⇒ x = 16 + 28
⇒ x = 44 years
Thus, their present age of father is 44 years and of daughter is 14 years.
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x=50
y=22
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