Question

Divide $Rs.750$ in the ratio $2:3$ between Ravi and Raju.

Answer 1

Hint:
Here, we will assume the constant of the ratio of amount of money with Ravi and Raju to be some variable. Adding the amount of both Ravi and Raju together and equating it to the total amount we will find the value of the assumed variable. Using the value of the variable we will find the amount of money with Ravi and Raju respectively.

Complete step by step solution:
Let the constant of the given ratio $2:3$ be $x$.
According to the question, we have to divide ${\text{Rs}}750$ in the ratio $2:3$ between Ravi and Raju.
Now, since the constant of the ratio is $x$.
Therefore,
Amount of money with Ravi $ = 2x$
Amount of money with Raju $ = 3x$
Here, we are required to divide the total amount of money ${\text{Rs}}750$ between them. We can write this mathematically as:
$2x + 3x = 750$
This is because when we add the money divided between them together, we will get the total amount.
Thus, solving this linear equation further, we get,
$ \Rightarrow 5x = 750$
Dividing both sides by 5, we get
$ \Rightarrow x = 150$
Therefore, the amount of money with Ravi $ = 2x = 2 \times 150 = {\text{Rs}}300$
And the amount of money with Raju $ = 3x = 3 \times 150 = {\text{Rs}}450$

Hence, we have divided ${\text{Rs}}750$ in the ratio $2:3$ between Ravi and Raju and they get ${\text{Rs}}300$ and ${\text{Rs}}450$ respectively.

Note:
An alternate way of finding their respective amounts is:
Since, we have to divide ${\text{Rs}}750$ in the ratio $2:3$ between Ravi and Raju
Thus, Ravi will get $\dfrac{2}{{2 + 3}} = \dfrac{2}{5}$ of the total amount
And, Raju will get $\dfrac{3}{{2 + 3}} = \dfrac{3}{5}$ of the total amount
Therefore,
Amount of money with Ravi $ = \dfrac{2}{5} \times 750$
Dividing 750 by 5, we get
Amount of money with Ravi $ = 2 \times 150 = {\text{Rs}}300$
And, amount of money with Raju $ = \dfrac{3}{5} \times 750$
Dividing 750 by 5, we get
Amount of money with Raju $ = 3 \times 150 = {\text{Rs}}450$
Hence, we have divided ${\text{Rs}}750$ in the ratio $2:3$ between Ravi and Raju and they get ${\text{Rs}}300$ and ${\text{Rs}}450$ respectively.
Thus, this is the required answer.