Question

The present ages of three persons in proportions $4:7:9$. Eight years ago, the sum of their ages was 56. Find their present ages in years.

Answer 1

Hint:As to find the present age we will get the relation by following the information given related to their sum of ages 8 years ago and ratio. As we will assume the present age to be $4x,7x$ and $9x$ further their ages sum 8 years ago was 56 through which we will get the relation between their ages and by using the substitution method we will get the present age.

Complete step-by-step solution:
Moving ahead with the question in step wise manner;
As at present their ages are in ratio$4:7:9$, so let us assume that there might be some common factor ‘x’ which might get reduced when ratio is being taken. So we can say that their age might be$4x,7x$and$9x$which will give ratio$4:7:9$when reduced to simpler ratios.
So we got their present age$4x,7x$and$9x$. Now according to other information given in the question , 8 years ago the sum of their ages is 56. As 8 years ago the ages would be;
$\begin{align}
  & 4x-8, \\
 & 7x-8, \\
 & 9x-8 \\
\end{align}$
And as we know that according to question sum of their ages is 56, so we can write it as;
$4x-8+7x-8+9x-8=56$
Simplifying it to find the value of ‘x’ we will get;
$\begin{align}
  & 20x-24=56 \\
 & 20x=56+24 \\
 & 20x=80 \\
 & x=\dfrac{80}{20} \\
 & x=4 \\
\end{align}$
So we got ‘x’ equal to 4. Now to find the present age of three persons, as we know that they have present age $4x,7x$ and $9x$. So put the value of ‘x’ in this, in order to get their present age. So it would be;
Present age of 1st person$=4x=4\times 4=16$ years. So the present age of the first person is $16$ years.
Similarly the present age of the 2nd person is $7x=7\times 4=28$. So the present age of a second person is $28$ years.
Similarly the present age of 3rd person is$9x=9\times 4=36$. So the present age of a third person is $36$years.
Hence answer is $16$ years, $28$ years and $36$ years of three persons whose present age ratio is $4:7:9$.

Note: If two or more values are placed as a ratio then there would be some common factor which got reduced from the values to make it a simpler ratio, which we assumed as ‘x’ in our case and came out to be $4$.