Question

The average age of 3 sisters is 15. If the ages of 2 sisters are 12 years and 15 years, the age of the third sister is
1) 21 years
2) 17 years
3) 18 years
4) 16 years

Answer 1

Hint: Here, we will use the formula to calculate the average is by dividing the sum of the terms by the number of the terms, that is, \[{\text{Average}} = \dfrac{{{\text{Sum of the terms}}}}{{{\text{Number of terms}}}}\].
Apply this formula of average and then use the given conditions to find the required value.

Complete step-by-step answer:

We are given that the average age of 3 sisters is 15 and the ages of 2 sisters are 12 years and 15 years.

Let us assume that the age of the third sister is \[x\] years.

We know that the formula to calculate the average is by dividing the sum of the terms by the number of the terms, that is, \[{\text{Average}} = \dfrac{{{\text{Sum of the terms}}}}{{{\text{Number of terms}}}}\].

We will now find the sum of the terms from the given ages of the three sisters.

\[12 + 15 + x = 27 + x\]

Now we will find the total number of terms.

3

Substituting the above values from the sum of the given numbers and total number of terms in the formula of average, we get

\[{\text{Average}} = \dfrac{{27 + x}}{3}\]

Since we know that the average of the given numbers is 15.

Replacing 15 for Average in the above equation, we get

\[15 = \dfrac{{27 + x}}{3}\]

Multiplying the above equation by 3 on each of the sides, we get

\[
   \Rightarrow 15 \times 3 = 3\left( {\dfrac{{27 + x}}{3}} \right) \\
   \Rightarrow 45 = 27 + x \\
 \]

Subtracting the above equation by 27 on each of the sides, we get

\[
   \Rightarrow 45 - 27 = 27 + x - 27 \\
   \Rightarrow 18 = x \\
   \Rightarrow x = 18 \\
 \]

Thus, the value of \[x\] is 18.

Therefore, the age of the third sister is 18.

Hence, option C is correct.

Note: While solving this question, we have to assume the age of the third sister by any variable and then solve the question using the same variable. In solving these types of questions, the important point to remember is that we need to have a good understanding of how to compute the average of some numbers. Also, we should be able to solve all the linear equations in just one variable, which will help us in simplifying this question.