Question

Rs. 3,000 is divided among A. B and C. such that A receives 1 : 3 as B and C together receive and B receives 2 : 3 as much as A and C together receive. Then the share of C is
(a) Rs 525
(b) Rs 1,625
(c) Rs 1050
(d) Rs 600

Answer 1

Hint: We will be using the concept of a system of equations to solve the equation. We will be forming the equations as per the question and solve them for the solution.

Complete step-by-step solution
We have been given that Rs 3000 is divided among A, B and C. Also it has been given to us that A receives 1 : 3 as much as B and C together. Let us take a, b, c be the money A, B, C respectively has therefore,
$a={\displaystyle \frac{1}{3}}(b+c)..........(i)$
Also, we have been given that B receives 2 : 3 as much as A and C together receive therefore
$b={\displaystyle \frac{2}{3}}(a+c)........\left(ii\right)$
Also, we have been given that A, B, C receive toral Rs 3000 therefor
$a+b+c=3000\dots \dots \dots (iii)$
Now we will solve equation (i), (ii) and (iii) for a, b and c. So, we have
$\Rightarrow 3a=b+c$
$\Rightarrow 3b=2a+2c$
$\Rightarrow a+b+c=3000$
Now we will substitute value of b + c from (i) into (iii)
$3a+a=3000$
$\Rightarrow 4a=3000$
$\Rightarrow a=750$
Also, we will put value of a + c from (ii) and (iii)
$\begin{array}{rl}& \Rightarrow b+{\displaystyle \frac{3}{2}}b=3000\\ & \Rightarrow {\displaystyle \frac{5}{2}}b=3000\\ & \Rightarrow b=600\times 2\\ & \Rightarrow b=1200\end{array}$
Now we will substitute the value of a = 750 and b = 1200 in (iii) to find c. So we have
$\Rightarrow 1200+750+c=3000$
$\Rightarrow c=3000–1950$
  $=Rs1050$
Therefore, the share of C is Rs 1050. Hence option (c) is correct.

Note: To solve these types of questions it is important to form an equation as per the data given in the question and solve them to find the answer. Also, one must note that the number of equations must be equal to the number of unknown variables to solve them.