Question

The cost of \[5\dfrac{3}{5}\]kg of sugar is Rs. \[50\dfrac{3}{{10}}\].What is the cost of 1 kg of sugar.

Answer 1

Hint: Converting mixed fraction into simplest form. Let us consider a mixed fraction \[2\dfrac{3}{5}\]. To convert it into the simplest form write\[2\dfrac{3}{5}\]=\[2 + \dfrac{3}{5}\].
Take L.C.M and solve the question.

Complete step-by-step answer:
Given price of sugar= Rs. \[50\dfrac{3}{{10}}\]
In simplest form, price of sugar can be written as=\[50\dfrac{3}{{10}}\]=\[\dfrac{{50 \times 10 + 3}}{{10}} = \dfrac{{500 + 3}}{{10}} = \dfrac{{503}}{{10}}\]Rs.
Given quantity of sugar=\[5\dfrac{3}{5}\]kg
In simplest form, quantity of sugar can be written as=\[5\dfrac{3}{5} = \dfrac{{5 \times 5 + 3}}{5} = \dfrac{{25 + 3}}{5} = \dfrac{{28}}{5}\]kg
\[\dfrac{{28}}{5}\]kg of sugar equals Rs. \[\dfrac{{503}}{{10}}\]
Cost of 1kg of sugar=Rs\[\dfrac{{\dfrac{{503}}{{10}}}}{{\dfrac{{28}}{5}}} = \dfrac{{503}}{{10}} \times \dfrac{5}{{28}}\]=8.98 Rs/kg.

Note: If the price of x kg of articles is Rs.y, then the price of 1 kg =Rs.y/x. Mixed fraction is the simplest way to express an improper fraction, in which the numerator is bigger than the denominator.