Question

Divide Rs. 1350 between Ravish and Shikha in the ratio \[2:3\] and find the amount each gets.

Answer 1

Hint: We solve this problem by using the definition of ratios. If a number \['n'\] is divided between two persons in the ratio \[a:b\] then there exists a number \['x'\] such that
\[\Rightarrow ax+bx=n\]
Here, we have a = 2, b = 3 and n = 1350. Also, we can say that the first person gets the number \['ax'\] and the second person gets \['bx'\]

Complete step by step solution:
We are given that the amount to be shared is Rs. 1350
Let us assume that the amount as
\[\Rightarrow n=1350\]
We are given that the amount is to be shared in the ratio \[2:3\]
We know that the definition of ratios that is if a number \['n'\] is divided between two persons in the ratio \[a:b\] then there exists a number \['x'\] such that
\[\Rightarrow ax+bx=n\]
Also, we can say that the first person gets the number \['ax'\] and the second person gets \['bx'\]
By using this definition to given problem we get
\[\begin{align}
  & \Rightarrow 2x+3x=1350 \\
 & \Rightarrow 5x=1350 \\
 & \Rightarrow x=270 \\
\end{align}\]
Let us assume that the amount Ravish gets as \[{{A}_{1}}\]
Now, by using the definition of ratios the amount Ravish gets is given as
\[\Rightarrow {{A}_{1}}=2x\]
Now, by substituting the value of \['x'\] in above equation we get
\[\begin{align}
  & \Rightarrow {{A}_{1}}=2\times 270 \\
 & \Rightarrow {{A}_{1}}=540 \\
\end{align}\]
Here, we can say that Ravish gets Rs. 540.
Let us assume that the amount Shikha gets as \[{{A}_{2}}\]
Now, by using the definition of ratios the amount Shikha gets is given as
\[\Rightarrow {{A}_{2}}=3x\]
Now, by substituting the value of \['x'\] in above equation we get
\[\begin{align}
  & \Rightarrow {{A}_{2}}=3\times 270 \\
 & \Rightarrow {{A}_{2}}=810 \\
\end{align}\]
Here, we can say that Shikha gets Rs. 810.
Therefore, when Rs. 1350 is divided among Ravish and Shikha in the ratio \[2:3\] then they get Rs. 540 and Rs. 810 respectively.

Note: We have a shortcut for solving this problem.
If the number \['n'\] is divided between two persons in the ratio \[a:b\] then the number that first person gets is
\[{{n}_{1}}=\left( \dfrac{a}{a+b} \right)n\]
Similarly, the number that second person gets is
\[{{n}_{2}}=\left( \dfrac{b}{a+b} \right)n\]
Let us assume that the amount Ravish gets as \[{{A}_{1}}\]
Now, by using the above formula of ratios the amount Ravish gets is given as
\[\begin{align}
  & \Rightarrow {{A}_{1}}=\left( \dfrac{2}{2+3} \right)1350 \\
 & \Rightarrow {{A}_{1}}=2\times 270=540 \\
\end{align}\]
Here, we can say that Ravish gets Rs. 540.
Let us assume that the amount Shikha gets as \[{{A}_{2}}\]
Now, by using the above formula of ratios the amount Shikha gets is given as
\[\begin{align}
  & \Rightarrow {{A}_{2}}=\left( \dfrac{3}{2+3} \right)1350 \\
 & \Rightarrow {{A}_{2}}=3\times 270=810 \\
\end{align}\]
Here, we can say that Shikha gets Rs. 810.
Therefore, when Rs. 1350 is divided among Ravish and Shikha in the ratio \[2:3\] then they get Rs. 540 and Rs. 810 respectively.