Question

Shanti has 3 daughters. The average age of them is 15 years. Their ages are in ratio 3:5:7. The age of youngest daughter ( in years)

Answer 1

Hint: We know the formula for average. The formula of average is sum divided by the number of units.
In this question it is given that their average is 15 and the ratio of their age is given after solving the equation we will get the correct answer i.e. age of youngest daughter.

Complete step-by-step answer:
It is given that shanty has has 3 daughters and their ages are in ratio 3:5:7
Then age of daughters A, B and C will be 3x, 5x and 7x
It is given that the average age of them is $$15$$ .
After formulating it will be like
$$\eqalign{
  & \dfrac{{3x + 5x + 7x}}{3} = 15 \cr
  & \Rightarrow \dfrac{{15x}}{3} = 15 \cr
  & \Rightarrow x = \dfrac{{15 \times 3}}{{15}} \cr
  & \Rightarrow x = 3 \cr} $$
Ages of their daughter will be
$$\eqalign{
  & 5x = 5 \times 3 = 15 \cr
  & 3x = 3 \times 3 = 9 \cr
  & 7x = 7 \times 3 = 21 \cr} $$
Hence, Age of the youngest daughter will be 9 years.
Note: We already knew the formula for average, which is a sum divided by number of units. In this problem we knew the average and ratio of their ages. We took x as common multiple. And after putting values in formula, we equate both sides i.e. LHS and RHS. After equating we got the correct answer.