Question

The present age of Sita’s father is three times the present age of Sita. After six years, the sum of their ages will be 69 years. Find their present ages.

Answer 1

Hint: Here, we need to find the present ages of Sita and her father. We will assume the present age of Sita and her father to be \[x\] and \[y\] respectively. We will use the given information to form two equations. Then, we will solve these equations to get the present ages of Sita and her father.

Complete step-by-step answer:
Let the present age of Sita and her father be \[x\] and \[y\] respectively.
The ages of Sita and her father 6 years later will be 6 more than their present ages.
Thus, we get the ages of Sita and her father after 6 years as \[x + 6\] and \[y + 6\] respectively.
Now, it is given that the present age of Sita’s father is 3 times Sita’s present age.
Thus, we get the equation
\[y = 3x\]
The sum of the ages of Sita and her father after 6 years is 69 years.
Thus, we get the equation
\[x + 6 + y + 6 = 69\]
Adding the terms, we get
\[ \Rightarrow x + y + 12 = 69\]
Subtracting 12 from both sides of the equation, we get
\[\begin{array}{l} \Rightarrow x + y + 12 - 12 = 69 - 12\\ \Rightarrow x + y = 57\end{array}\]
Now, we will solve the two equations to get the values of \[x\] and \[y\], and hence, the present ages of Sita and her father.
Substituting \[y = 3x\] in the equation \[x + y = 57\], we get
\[\Rightarrow x+3x=57\]
Adding the like terms, we get
\[ \Rightarrow 4x = 57\]
Dividing both sides by 4, we get the value of \[x\] as
\[ \Rightarrow x = \dfrac{{57}}{4} = 14.25\]
Therefore, the present age of Sita is \[14.25\] years.
Substitute \[14.25\] for \[x\] in the expression \[y = 3x\], we get
Present age of Sita’s father \[ = 3x = 3 \times 14.25 = 42.75\] years
Therefore, we get the present ages of Sita and her father as \[14.25\] years (14 years 3 months) and \[42.75\] years (42 years 9 months) respectively.

Note: We added the like terms in a step of the solution. Like terms are those terms which consist of variables that are the same and are raised to the same exponent. For example, \[100x,150x,240x,600x\] all have the variable \[x\] raised to the exponent 1. Unlike terms are opposite of like terms and cannot be added together. For example, we cannot add 1 to \[3x\], but we can add \[x\] to \[3x\].
We can verify the answer by using the information given in the question..
Sita’s age 6 years later will be \[14.25 + 6 = 20.25\] years.
Sita’s father’s age 6 years later will be \[42.75 + 6 = 48.75\] years.
Now, we can observe that \[20.25 + 48.75 = 69\].
Therefore, we have verified that the sum of their ages 6 years later is 69 years.
Hence, we have verified our answer.