Question

If an amount of $150,000$ is shared between $A,B$ and $C$ in the ratio $2:3:5$, then $A$ receives the same amount as he would receive if another sum of money is shared between $A,B$ and $C$ in the ratio $5:3:2$. The ratio of $150,000$ to the second amount of money is
$\text{A) 2:3}$
$\text{A) 3:2}$
$\text{C) 5:3}$
$\text{D) 5:2}$

Answer 1

Hint: In this question we have been given two sets of data about the money shared between $A,B$ and $C$, and their ratios. We will first find out how much money out of $150,000$ belongs to $A$. We will then use this amount to find the second amount which belongs to $A$ and then find out the ratio of the amount $150,000$ to the second amount which belongs to $A$.

Complete step by step solution:
We know that the amount $150,000$ is shared between $A,B$ and $C$ in the ratio $2:3:5$ therefore the amount which belongs to $A$ will be:
since $A$ has the ratio $2$, and $2+3+5$ gives us the total amount of money.
$\Rightarrow Rs.150,000\times \dfrac{2}{2+3+5}$
On simplifying, we get:
$\Rightarrow Rs.150,000\times \dfrac{2}{10}$
On simplifying the fraction and multiplying, we get:
$\Rightarrow Rs.30,000$
Now in the second case, we don’t know the total amount of money therefore, lets consider it as $x$.
The shares in the amount are in the ratio $5:3:2$ .
since $A$ has the ratio $5$, and $5+3+2$ gives us the total amount of money.
therefore, $A's$ share will be:
$\Rightarrow Rs.x\times \dfrac{5}{5+3+2}$
On simplifying, we get:
$\Rightarrow Rs.x\times \dfrac{5}{10}$
On simplifying the fraction, we get:
$\Rightarrow Rs.\dfrac{x}{2}$
Now we know from the question that this amount is the same amount as the previous amount therefore, we get:
$\Rightarrow Rs.\dfrac{x}{2}=Rs.30,000$
On simplifying, we get:
$\Rightarrow x=Rs.60,000$, which is the second amount.
Now the ration between $Rs.150,000$ and the second amount $Rs.60,000$ will be:
$\Rightarrow 150,000:60,000$
On simplifying, we get:
$\Rightarrow 5:2$

So, the correct answer is “Option D”.

Note: Ratio is based on the concept of fractions, a ratio is basically a fraction in the form of $\dfrac{a}{b}$ represented as $a:b$. It is used to represent a value in terms of another value.
Proportion is a concept in ratio and it represents when two ratios are the same.
A ratio of two fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$ can be represented as $a:b::c:d$.