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: In this question, we have to calculate the amounts for the particular required.
We need to find first the ratio of ages so that we get the amounts for the particular required.
Then we will take a random variable as the amount of Shreya then subtract it from the total amount we will get the amount for Bhoomika in terms of the random variable. Equating the original ratio and the ratio of random variables we will get the value of the random variable. Then we will get the required answer.

Complete step-by-step answer:
It is given that, Mother wants to divide Rs.\[36\] between her daughters Shreya and Bhoomika in the ratio of their ages.
Also given that, the age of Shreya is \[15\] years and the age of Bhoomika is \[12\] years.
We need to find out the amount Shreya and Bhoomika will get.
The ratio of Shreya’s age : Bhoomika’s age = \[15:12 = 5:4\]
Let, Shreya will get Rs. \[x\] after dividing Rs.\[36\] between Shreya and Bhoomika in the ratio of their ages.
Then Bhoomika will get Rs. \[36 - x\].
The ratio of Shreya’s age: Bhoomika’s age in terms of random variable = \[x:36 - x\]
Equating these two ratios we get,
\[ \Rightarrow 5:4 = x:36 - x\]
\[ \Rightarrow \dfrac{5}{4} = \dfrac{x}{{36 - x}}\]
By cross multiplication we get,
\[ \Rightarrow 180 - 5x = 4x\]
Taking the random variables in the same side,
\[ \Rightarrow 5x + 4x = 180\]
Solving the equation for \[x\],
\[ \Rightarrow 9x = 180\]
\[ \Rightarrow x = \dfrac{{180}}{9} = 20\]
Hence, Shreya will get Rs.\[20\] and Bhoomika will get Rs.\[36 - 20 = Rs.16\].

Note: A ratio shows the relative sizes of two or more values.
Ratios can be shown in different ways:
Using the ":" to separate example values.
Using the "/" to separate one value from the total.
As a decimal, after dividing one value by the total.
As a percentage, after dividing one value by the total.