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Four years ago, the father's age was three times the age of his son. The total of the ages of the father and the son after four years will be 64 years. What is the father's age at present?
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Father's present age = $40$ years
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Son's present age = $16$ years
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The correct answers are 16 and 40.
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\begin{align}\text{At present, father's age = x years}\\ \text{& son's age = y years} \end{align}

\begin{align}\text{∴ 4 years ago, father's age would be (x-4) years} \\ \text{ & son's age would be (y-4) years} \end{align}

Now, given that,

Four years ago, the father's age was three times the age of his son.

$∴ (x-4) = 3(y-4) ---------- 1)$

Also given that,

The total of the ages of the father and the son $\underline{\text{after four years}}$ will be 64 years.

$∴ ( x+4 )+ (y+4 ) = 64 \\Or, x = 64 - 8 - y \\ Or, x = 56 - y ------ 2)$

Now, putting the $x's$ value in the equation $1)$

$(x-4) = 3(y-4) \\ Or, 56-y-4 = 3y - 12 \\ Or, 52-y = 3y-12 \\ Or, 52+12 = 3y+y \\ Or, 4y = 64 \\ Or, y = \dfrac{64}{4} = 16$

$\color{maroon}{\text{∴ Son's present age is 16 years}}$

Now, putting the value of $y = 16$ in equation $2)$, we get -

$x = 56 - y \\ = 56 - 16 \\ = 40$

$\color{green}{\text{∴ Father's present age is 40 years. }}$

by (2.5k points) 5 9 19
edited
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This is wrong. The correct answers are 16 and 40. Will be means that the question is talking about future.
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@subarna , you have not added +4 in equation (2) for "after 4 years"..
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ankitgupta.1729 yeah, i missed the line $\underline{\text{after four years}}$

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Now, corrected
+1 vote

Assum father's present age to be $x$ $years$ and son's present age to $y$ $years$.

Four years ago father's age is 3 times the age of his son means:

$x - 4 = 3(y-4)$

The total of the ages of the father and the son after four years will be 64 years. Will be means that the question is talking about future, and therefore the correct second equation is:

$x + 4 + y + 4 = 64$

Solving the two equations we get $x = 40$, father is presently $40$ years old and $y = 16$, son is presently $16$ years old.

by (38 points) 1 1
Let present son age is x and father age is y.

From given data,

y-4=3(x-4)

=>y-4=3x-12

=> 3x-y-8=0                                  -------→  “1”

and also given

x+4+y+4=64

=> x+y-56=0                                 --------→ “2”

simplyfing 1 and 2 we get x=16 and y= 40 which means father age is 40.
by (54 points) 1
by (44 points) 1 1 3

+1 vote