Question

Mother wants to divide Rs.36 between her daughters Shreya and Bhoomika in the ratio of their ages. If the age of Shreya is 15 years and the age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get?

Answer 1

Hint: Take Shreya’s and Bhoomika’s amounts as variables by using the total amount belonging to their mother. Now, calculate the fractions of the amounts supposed w.r.t variable and fraction of their given ages. Now, use the given condition by her mother to get the variable and hence amounts belong to Shreya and Bhoomika.

Complete step-by-step solution -
Let us suppose Shreya will get Rs.x out of the total money Rs.36, so Bhoomika will definitely get Rs.(36 – x).
Now, we know that mother wanted to divide the whole amount of Rs.36 between her daughters Shreya and Bhoomika in the ratio of their ages.
So, the ratio of money Rs.x and Rs.(36 – x) will be equal to the ratio of their ages. The ages of Shreya and Bhoomika are given as 15 years and 12 years respectively.
So, ratio of amounts of Shreya and Bhoomika in terms of ‘x’ would be given as,
$\dfrac{x}{36-x}$
The ratio of the ages can be given as,
 $\dfrac{15}{12}$.
Now, we can equate both the ratios as both are representing the ratio of amounts divided between Shreya and Bhoomika, so we get
$\dfrac{x}{36-x}=\dfrac{15}{12}.....................\left( i \right)$
Now, we can find the values of ‘x’ from the above equation by cross-multiplying the relation. Hence, on cross multiplying the equation (i), we get
$x\times 12=15\times \left( 36-x \right)$
$\begin{align}
  & 12x=15\times 36-15x \\
 & \Rightarrow 12x+15x=15\times 36 \\
 & \Rightarrow 27x=15\times 36 \\
\end{align}$
Now, we can divide the whole equation by 27 to get the value of ‘x’, we get
$\begin{align}
  & \dfrac{27}{27}x=\dfrac{15\times 36}{27} \\
 & \Rightarrow x=\dfrac{15\times 36}{27}=\dfrac{15\times 4}{3} \\
 & \Rightarrow x=5\times 4=20 \\
\end{align}$
Now, as we have assumed the amounts of Shreya and Bhoomika as Rs.x and Rs.(36 – x). Hence, Shreya will get Rs.20 out of Rs.36 by her mother.
Therefore, Bhoomika will get (36 – 20) =Rs. 16
Therefore, Shreya and Bhoomika will get Rs.20 and Rs.16 respectively.

Note: One can take two variables x and y for representing the amounts belong to Shreya and Bhoomika and get equations as,
x + y = 36 and $\dfrac{x}{y}=\dfrac{15}{12}$
Now, solve both the equations to get x and y individually. This can be another approach for the given question. One can go wrong when assuming the amount of Bhoomika after Shreya’s amount as ‘x’ in solution. One may assume the amount of Bhoomika as Rs.(x – 36) which is wrong, as the total amount cannot be less than an individual amount.