Question

Find the ratio of the price of coffee to that of tea when coffee costs Rs.24 per 100 g and tea costs Rs.80 per kilogram.

Answer 1

Hint: Type of question is based on finding out ratio of quantity or of some value. The concept says if we need to find out the ratio of some measurable quantity or of value then that value or quantity must be with the same unit. As in the question it is asked to find out the ratio of price of coffee to that of tea, which is Rs.24 per 100 g and Rs.80 per kilogram respectively. As both these prices have different units, one is in grams and other is in kilogram, so we need to make them the same and simplify them to have a simpler ratio.

Complete step by step answer:
So moving ahead with the question we had,
Price of coffee is $ = $ Rs.24 per 100 g
So price of coffee for one gram is
 \[\begin{align}
  & =\dfrac{24}{100} \\
 & =0.24Rs \\
\end{align}\]
Price of tea is $ = $ Rs.80 per kilogram.
So price of tea for one gram is
 $ \begin{align}
  & =\dfrac{80}{1000} \\
 & =0.08Rs \\
\end{align} $
So we can say that the price of one gram coffee is 0.24Rs and the price for one gram of tea is 0.08Rs. As now both items have a price for the same unit i.e. for one gram. So now the ratio of price of coffee to tea is equal to price of coffee upon price of tea that is equal to
 \[\begin{align}
  & =\dfrac{0.24}{0.08} \\
 & =\dfrac{24}{8} \\
 & =\dfrac{3}{1} \\
\end{align}\]
Hence \[\dfrac{3}{1}\] is the ratio of the price of coffee to the price of tea.

Note: \[\dfrac{3}{1}\] can also be written as $ 3:1 $ both answers are correct. Moreover keep in mind that you place the right value in the numerator and denominator while taking the ratio, as for the value we use to that, is placed in the denominator, for example as we did in our case.