Question

A sum of money is divided among Peter, Anita and Janet in the ratio $13:12:7$. Calculate how much Anita gets, if the amount Peter gets more than Janet is Rs. $360?$
Rs. $180$
Rs. $640$
Rs. $720$
Rs. $480$

Answer 1

Hint: Identify the known and unknown ratios and set up the proportion and solve accordingly.

Complete step-by-step answer:
In these ratio types of questions, take any variable as the reference number.
Given that: A sum of money is divided among Peter, Anita and Janet in the ratio $13:12:7$
Let us, suppose that “x” is the common number
So, Peter gets $13x$ Money
Anita gets $12x$ Money
Janet gets $7x$ Money
Peter gets more than Janet $= 360$
$13x = 7x + 360$
Taking on left hand side,
$\begin{array}{l} 13x - 7x = 360\\\ \Rightarrow 6x = 360\\\ \Rightarrow x = \dfrac{{360}}{6}\\\ \Rightarrow x = 60 \end{array}$
Anita gets $12x$ Money,
Put, $x = 60$
$\begin{array}{l} 12x = 12(60)\\\ 12x = 720 \end{array}$
Therefore, Anita gets 720 rupees.
This is the required answer.
Hence, the option C is the correct answer.

Additional Information: Ratio is the comparison between two numbers without any units.
Whereas, when two ratios are set equal to each other are called proportion.
Four numbers a,b,c,and d are said to be in proportion. If $a:b = c:d$whereas, four numbers are said to be in continued proportion if $a:b = b:c = c:d$

Note: When solving these type of questions, do not stop the question after finding the value of x; please find the other values which are asked too.