Question

The average age of 3 girls is 20 years and their ages are in proportion $3:5:7$, the age of youngest girl is
(a)8 years 3 months
(b)6 years 8 months
(c)12 years
(d)20 years

Answer 1

Hint: Find the total age of 3 girls from the given average age. Take \[x\] as the age. Thus, find the age of the girl and equal it to total age. Solve for \[x\]. Then out of all the 3 girls, find the youngest girl.

Complete step-by-step answer:
It is given that the average age of three girls is 20 years.
Thus, the total age of the three girls \[=\ 20\ \text{years}\times 3\ =\ 60\ \text{years}\]
\[\therefore \] The total age of the three girls \[=\ 60\ \text{years}\]
Now, the ages of the three girls are in proportion $3:5:7$.
Thus, let us consider the age as ‘\[x\]’.
\[\therefore \]The age of 1st girl \[=\ 3x\]
     Age of 2nd girl \[=\ 5x\]
     Age of 3rd girl \[=\ 7x\].
Now, the total age of the 3 girls \[=\ 60\]
\[\therefore \text{ }3x+5x+7x\ =\ 60\]
\[15x\ =\ 60\ \Rightarrow \ x\ =\ \dfrac{60}{15}\ =\ 4\]
Hence, we got \[x\ =\ 4\]
The age of 1st girl \[=3x\ =\ 3\times 4\ =\ 12\]
Age of 2nd girl \[=5x\ =\ 5\times 4\ =\ 20\]
The age of the 3rd girl \[=7x\ =\ 7\times 4\ =\ 28\]
Out of this the youngest girl is of the age 12.
\[\therefore \] The age of the youngest girl \[=\ 12\ \text{years}\]
\[\therefore \] Option (c) is the correct answer.

Note:We know what an average is, it is the result obtained by adding several numbers together and then dividing this by the total no.’s. Thus, here it is the average of 3 ages. Thus, total age will be \[3\times \text{average}\] age given.