Question

A person earns \[Rs.100\] in a day. If he spends \[Rs.14\dfrac{2}{7}\] on food and \[Rs.30\dfrac{2}{3}\] on petrol. How much did he save on that day?

Answer 1

Hint:Mixed fractions should be changed into improper fractions first. The total amount spent by the person should be subtracted to the total amount earned by him to get the saving by him on that day. Addition and subtraction of fractions is done after taking the L.C.M. (Least Common Multiple) of the denominators.

Complete step by step answer:
We are given that a person earns \[Rs.100\] in a day and spends \[Rs.14\dfrac{2}{7}\] and \[Rs.30\dfrac{2}{3}\] on food and petrol respectively. We have to find out the total amount of money saved by him on that day. For this we should first add the total amount of money spent by him on the day and then subtract it from the total amount he earned that day.
Given, total amount earned \[ = Rs.100\]
Amount spend on food\[ = Rs.14\dfrac{2}{7}\]
Converting the above mixed fraction into improper fraction. We get,
\[14\dfrac{2}{7} = \dfrac{{14 \times 7 + 2}}{7}\]
On simplifying,
\[14\dfrac{2}{7} = \dfrac{98 + 2}{7} = Rs\dfrac{100}{7}\]
Amount spend on petrol \[ = Rs.30\dfrac{2}{3}\]

Converting the above mixed fraction into improper fraction. We get,
\[30\dfrac{2}{3} = \dfrac{{30 \times 3 + 2}}{3}\]
On simplifying,
\[30\dfrac{2}{3} = \dfrac{{90 + 2}}{3} = Rs.\dfrac{{92}}{3}\]
Now, adding the above two expenditures on food on petrol we get the total amount spent by the person. So, on adding we get,
Total spent amount \[ = {\text{ Rs}}{\text{.}}\,\dfrac{{100}}{7} + \dfrac{{92}}{3}\]
Taking L.C.M. of denominators of both fraction that is L.C.M. of \[7\] and \[3\] is \[21\] and adding fractions
Total spent amount\[ = {\text{ Rs}}{\text{.}}\,\dfrac{{100 \times 3 + 92 \times 7}}{{21}}\]
On multiplying and adding,
Total spent amount \[ = Rs.{\text{ }}\dfrac{{300 + 644}}{{21}} = Rs.\,\,\dfrac{{944}}{{21}}\]

Now,
\[\text{The amount saved by the person = Total amount earned by him - Total amount spend by him} \]
Hence, the total amount saved by the person \[ = {\text{ }}Rs.100 - Rs.\,\dfrac{{944}}{{21}}\]
Again taking L.C.M. and solving we get,
The total amount saved by the person \[ = {\text{ }}Rs.\dfrac{{100 \times 21 - 944}}{{21}}{\text{ }} = {\text{ }}Rs.\dfrac{{1156}}{{21}}\]
Converting it into mixed fraction we could write it as \[\dfrac{{1156}}{{21}} = \dfrac{{55 \times 21 + 1}}{{21}} = {\text{ }}55\dfrac{1}{{21}}\]

Hence, the person saved \[Rs.\,\,55\dfrac{1}{{21}}\] on that day.

Note:Addition and subtraction of fractions are only done after equalling the denominators of fraction by taking L.C.M. Fractions also follow the BODMAS (Bracket Order Division Multiplication Addition Subtraction) rule for arithmetic operations irrespective of any numerical values. Mixed fractions must be changed to improper fractions for smooth and precise calculation.