Question

If 9 kg of rice costs Rs.120.60, what will 50 kg of such quality rice cost?

Answer 1

Hint: To solve this question, we should know the concept of proportionality of two parameters. Here, in the question, the number of kg of rice is directly proportional to the cost of that much kg rice. From this principle, we can get the cost of 1 kg of rice and then multiply it with 50 to get the cost of 50 kg of rice.

Complete step-by-step solution:
Consider two parameters F and G which are directly proportional to each other. This means that F increases or decreases linearly with G increasing or decreasing respectively. Numerically, directly proportional is shown as $F\propto G$. As the two parameters are linearly related, we can assume a constant of proportionality K which is used to get an equation.
$\begin{align}
  & F\propto G \\
 & F=KG\to \left( 1 \right) \\
\end{align}$
By using the initial condition, we can find the constant of proportionality and we can find the required answer.
In the question, let
G – Number of kg of rice purchased
F – Cost of G kg of rice.
From equation-1
Cost of rice purchased = K $\times $ Number of kg of rice purchased.
In the question, it is given that 9 kg of rice costs Rs.120.60
G = 9 kg, F = Rs.120.60
Substituting in equation-1, we get
$Rs.120.60=K\times 9kg$
Dividing by 9kg on both sides gives
$\begin{align}
  & K=\dfrac{120.60}{9}\dfrac{Rs}{kg} \\
 & K=13.40\dfrac{Rs}{kg} \\
\end{align}$
Equation-1 can be written as
$F=13.40G\to (2)$
We have to find the cost of 50 kg. So, G = 50. Substituting G = 50 in equation-2, we get
$\begin{align}
  & F=13.40\times 50 \\
 & F=134\times 5=670 \\
\end{align}$
$\therefore $The cost of 50 kg of the same quality rice is Rs.670

Note: The question can be solved in another way using the unitary method. The unitary method is a way in which we compare similar parameters and directly solve the question. That is if
A - B and
C - D then we can write that$\dfrac{A}{C}=\dfrac{B}{D}\to \left( 3 \right)$. Similarly,
9kg - Rs.120.60
50kg - $x$
Substituting in equation-3, we get
$\begin{align}
  & \dfrac{9}{50}=\dfrac{120.60}{x} \\
 & \\
\end{align}$
Cross-multiplying gives
\[\begin{align}
  & x=\dfrac{50\times 120.60}{9} \\
 & x=50\times 13.4 \\
 & x=Rs.670 \\
\end{align}\]
This tally with the answer in the process of the solution.