Question

A, B, C earn Rs. 1,980 in total. They earn it in ratio of 2 : 1 and 3 : 2 respectively, then B earned
A. Rs. 500
B. Rs. 520
C. Rs. 540
D. Rs. 560

Answer 1

Hint: Considering the amounts of A and B with a variable and similarly B and C with respect to another variable using the given ratios of the amounts.Now, equate the amount of B and convert amounts of each of A, B and C as a single variable. Now, add them and equate it to the given amount and calculate the money earned by B.

Complete step-by-step answer:
Here, the total money earned by A, B, C is 1980 Rs. in total and the ratio of earned money of A and B and B and C are given as 2 : 1 and 3 : 2 respectively.
So, we can use a variable ‘x’ to write the money for A and B. So, let 2x and x are the earned money for A and B respectively as the ratio of 2x and x is 2 : 1. So, we get,
Money earned by A = 2x.................................(i)
Money earned by B = x....................................(ii)
Now, we can use another variable ‘y’ to write the money for B and C. So, let 3y and 2y are the amounts of money earned by B and C respectively as the ratio of 3y and 2y will always be 3 : 2.
Now, we get,
Money earned by B = 3y.................................(iii)
Money earned by C = 2y....................................(iv)
Now, from equation (ii) and (iii), we get the money earned by B in two different variables i.e. x and 3y.
So, both should be equal as both are representing the same amount. So, we get,
x = 3y........................(v)
Now, we can write money earned by ‘A’ in terms of ‘y’ as well with the help of equation (i) and (v). So, we get,
Money earned by $A=2x=2\times 3y=6y.............\left( vi \right)$
Now, money earned by A, B, C in terms of variable ‘y’ are given by equations (vi), (iii) and (iv) respectively and the total amount earned by A, B and C is 1980 Rs. in total from the question. Hence, we can write equation as,
$\begin{align}
  & 6y+3y+2y=1980 \\
 & \Rightarrow 11y=1980 \\
 & \Rightarrow y=\dfrac{1980}{11}=180 \\
\end{align}$
Now, amounts of A, B, C can be given in terms of ‘y’ as 6y, 3y, 2y respectively. Hence, we get,
Amount earned by $A=6\times 180=1080$
Amount earned by $B=3\times 180=540$
Amount earned by $C=2\times 180=360$
Hence, 540 is the answer as it was asked in the question.
So, option C is correct.

Note: Taking 2x and x as amounts earned by A and B and 3y and 2y as amounts of B and C respectively by using the given ratio was the key point of the question.
One may convert the whole amounts of A, B, C in terms of ‘x’ as well by using the relation
$\begin{align}
  & x=3y \\
 & \Rightarrow y=\dfrac{x}{3} \\
\end{align}$
Hence, it can be another approach as well to find amounts.
One may use other variables for the amounts of A, B and C.
One can verify the solution by adding the calculated amounts earned by A, B and C in the question.