Question

The price of rice rises from Rs. 30 per kg to Rs. 36 per Kg. Find the percentage rise in the price of rice.

Answer 1

Hint: We first find the increase in value and its percentage form. We get fraction form and simplify it to find the final solution.

Complete step-by-step answer:
The price of rice rises from Rs. 30 per kg to Rs. 36 per Kg. The price is $ 36-30=6 $ per Kg.
The increase in percentage will be considered with respect to the first value of 30.
So, the percentage value will be $ \dfrac{6}{30}\times 100=\dfrac{600}{30} $ .
We need to find the simplified value of the fraction form.
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 give fraction $ \dfrac{600}{30} $ , the G.C.D of the denominator and the numerator is 30.
 $ \begin{align}
  & 2\left| \!{\underline {\,
  30,600 \,}} \right. \\
 & 3\left| \!{\underline {\,
  15,300 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5,100 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,20 \,}} \right. \\
\end{align} $
The GCD is $ 2\times 3\times 5=30 $ .
Now we divide both the denominator and the numerator with 30 and get $ \dfrac{{}^{600}/{}_{30}}{{}^{30}/{}_{30}}=20 $ .
Therefore, the percentage rise in the price of rice is 20.
So, the correct answer is “20%”.

Note: The value of the fraction is actually the unitary value of 20 out of 100. Therefore, in percentage value we got 20 as the percentage. Percentage deals with the ratio out of 100. The ratio value for both fraction and percentage is the same.