Question

Raman had 30 flowers. He offered some flowers in a temple and found that the ratio of a number of remaining flowers to that of flowers in the beginning is \[2:5\]. Find the number of flowers offered by him in the temple.

Answer 1

Hint:
Here, we will assume the numbers of flowers to be some variable. Then by using the given ratio, we will find the number of flowers, Then using this we will find the number of remaining flowers. We will then find the number of flowers offered by him in the temple by subtracting the number of remaining flowers from the total number of flowers.

Complete step by step solution:
We are given a total of 30 flowers at the beginning.
We are given that the ratio of a number of remaining flowers to that of flowers in the beginning is \[2:5\].
Let \[x\] be the number of flowers. So, we get
\[ \Rightarrow \] Number of remaining flowers \[ = 2x\]
\[ \Rightarrow \] Number of flowers at the beginning \[ = 5x\]
We are given that the total number of flowers is 30. So, we get
\[ \Rightarrow 5x = 30\]
By rewriting the equation, we get
\[ \Rightarrow x = \dfrac{{30}}{5}\]
\[ \Rightarrow x = 6\]
So, the number of remaining flowers \[ = 2x\]
\[ \Rightarrow \] Number of Remaining flowers \[ = 2\left( 6 \right) = 12\]
Number of flowers offered in the temple is found by subtracting the number of Remaining flowers from the total number of flowers.
\[ \Rightarrow \] Number of flowers offered in the Temple \[ = 30 - 12\]
\[ \Rightarrow \] Number of flowers offered in the Temple \[ = 18\]

Therefore, the number of flowers offered in the temple is 18.

Note:
Let \[x\] be the number of flowers offered in the temple.
We know that then the remaining number of flowers is \[30 - x\].
Number of flowers offered in temple \[ \div \] Total flowers \[ = \] Remaining flowers \[ \div \] Total flowers
We are given that the ratio of a number of remaining flowers to that of flowers in the beginning is \[2:5\].
 \[ \Rightarrow \dfrac{{30 - x}}{{30}} = \dfrac{2}{5}\]
By cancelling the terms, we get
\[ \Rightarrow \dfrac{{30 - x}}{6} = 2\]
Multiplying 6 on both sides, we get
\[ \Rightarrow 30 - x = 12\]
Subtracting 12 from both sides, we get
\[ \Rightarrow x = 30 - 12\]
\[ \Rightarrow x = 18\]
Therefore, the number of flowers offered in the temple is 18.