Question

Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
A. 16 years
B. 18 years
C. 28 years
D. 24.5 years
E. none of these

Answer 1

Hint:Assume the age of Sachin as ‘x’. Thus get the age of Rahul and form of relation connecting their present ages to 7:9. Use cross product property and find the value of x.

Complete step-by-step answer:
Let us assume the age of Sachin as ‘x’.
It is said that Rahul is 7 years older than Sachin. Therefore the age of Rahul is (x + 7).
Now the ages of Sachin and Rahul are given in the ratio 7:9. Thus we can say that \[x:x+7=7:9\].
Thus we can say that \[x:x+7=7:9\].
We can also write it as,
\[\dfrac{x}{x+7}=\dfrac{7}{9}\].
Now using cross product we can write that,
\[\begin{array}{*{35}{l}}
   9x=7\left( x+7 \right) \\
   9x=7x+49 \\
\end{array}\]
Now let us rearrange them and find the value of x.
\[\begin{align}
 & 2x=49 \\
 & x=\dfrac{49}{2}=24.5 \\
\end{align}\]
Thus the age of Sachin = x = 24.5
Age of Rahul = x + 7 = 24.5 +7 = 31.5
What we need is the age of Sachin which is 24.5
Thus we got the age of Sachin as 24.5 years.
Option D is the correct answer.

Note:We can take the age of Rahul as ‘x’ and that of Sachin as x-7. Thus the ratio becomes, \[x-7:x=7:9\], which can also be written as,
\[\begin{align}
  & \dfrac{x-7}{x}=\dfrac{7}{9}\Rightarrow 9\left( x-7 \right)=7x \\
 & 9x-63=7x \\
 & \therefore x={}^{63}/{}_{2}=31.5 \\
\end{align}\]
Thus the age of Rahul = x = 31.5 years.
Age of Sachin = x – 7 = 31.5 – 7 = 24.5 years.