Question

The sum of the ages of husband, wife and their two children is x years find their ages after 4 years.
$\begin{align}
  & \left( a \right)x+4 \\
 & \left( b \right)x+12 \\
 & \left( c \right)x+16 \\
 & \left( d \right)x+20 \\
\end{align}$

Answer 1

Hint: To solve the question given above, we will assume that the present age of husband is a, the present age of wife is b, the age of first child is c and the present age of second child is d. Thus with the help of information given in question, we will develop the relation between x, a, b, c and d and we will assume that the sum of the new ages is x. Thus we will develop a between $x'$and x.
Complete step by step solution:
To start with, we will assume that the present age of husband is a, the present age of wife is b, the present age of first children is c and the present age of second children is d. Also, it is given that the sum of their present ages is x. So, we will have the following relation:
$x=a+b+c+d..........\left( 1 \right)$
Now, the new age of husband is a’, the new age of wife is b’, the new age of first children is c’ and the new age of second children is d’. Also the new sum is x’. Thus, we have the following relation:
$x'=a'+b'+c'+d'...........\left( 2 \right)$
Now these new ages are the ages after 4 years. So, we will get:
$\begin{align}
  & a'=a+4.......\left( 3 \right) \\
 & b'=b+4........\left( 4 \right) \\
 & c'=c+4........\left( 5 \right) \\
 & d'=d+4.......\left( 6 \right) \\
\end{align}$
Now, we will put these values of a’, b’, c’ and d’ from (3), (4), (5) and (6) to (2). Thus, we will get:
$\begin{align}
  & \Rightarrow x'=\left( a+4 \right)+\left( b+4 \right)+\left( c+4 \right)+\left( d+4 \right) \\
 & \Rightarrow x'=a+b+c+d+16............\left( 7 \right) \\
\end{align}$
From (6) and (7), we get:
$\Rightarrow x'=x+16$
Hence, option (c) is correct

Note: We cannot calculate the individual ages of the husband, wife and two children because the data given in the question is very less. That’s why, instead of calculating the individual values of a, b, c and d, we have directly derived the relation between $x'$ and x.