Question

Find the cost of 8 Kg of rice if the cost of 5 Kg of rice is Rs. $ 107.50 $ .

Answer 1

Hint: We use the unitary system to find the cost of 1Kg rice. Then we multiply with 8 to find the required solution for the cost of 8 Kg of rice. We need the simplified answer of the fraction.

Complete step by step solution:
We are going to use the unitary system to find the cost of 8 Kg of rice.
From the cost of 5 Kg of rice is Rs. $ 107.50 $ , we find the cost of 1 Kg of rice.
Then we multiply with 8 to find the required solution.
So, the cost of 1 Kg of rice is $ \dfrac{107.5}{5} $ . Multiplying with 8 we get the cost of 8 Kg rice as $ \dfrac{107.5}{5}\times 8 $ .
So, $ \dfrac{107.5}{5}\times 8=\dfrac{860}{5} $ .
For any fraction $ \dfrac{p}{q} $ , we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $ \dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}} $ .
For our given fraction $ \dfrac{860}{5} $ , the G.C.D of the denominator and the numerator is 5.
 $ \begin{align}
  & 5\left| \!{\underline {\,
  5,860 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,172 \,}} \right. \\
\end{align} $
Now we divide both the denominator and the numerator with 5 and get $ \dfrac{{}^{860}/{}_{5}}{{}^{5}/{}_{5}}=172 $ .
Therefore, the cost of 8 kg rice is Rs. 172.
So, the correct answer is “Rs. 172”.

Note: In case we are having the value of multiple items with us, then we will simply divide the total value with the number of units to get the value of 1 unit and this process is known as the unitary method.