Question

The profits of a firm were Rs.72,000 in the year 2014. During the next year, it increased by 7% and it decreased by 5% in the following year. What are the profits of the firm after two years?

Answer 1

Hint: In the year after 2014, the profits were increased by 7%. So, first calculate the increased amount in profits for year 2015 and then calculate the total profits for year 2015. Now use the total profit data of year 2015 to calculate the profit data for year 2016.

Complete step-by-step answer:
In the question, it is given that profits for 2014 = Rs.72,000.
Now, for the next year i.e.2015, it is increased by 7%.
So, first of all we will calculate by what amount the profit increases.
The increased amount in profits for year 2015 as compared to year 2014 is given as:
$ 7\% of Rs.72000 = \dfrac{7}{{100}} \times {\text{Rs}}.72000$.=Rs.5040
So, the increased amount in profits in 2015=Rs.5,040.
The total profits for year 2015= profits of year 2014 + extra profits of year 2015.
                                                     =Rs.72,000 +Rs.5,040
                                                     = Rs.77,040.
Also, it is given that in the following year i.e. year 2016, there is a decrease in profits by 5%.
So, to calculate the decreased amount in profit in the year 2016, we will use the total profits in the 2015 which is Rs.77,040.
The decreased amount in profits for year 2016 is given as:
5% of Rs.77,040 = $\dfrac{5}{{100}} \times {\text{Rs}}{\text{.77,040 }}$= Rs.3,852.
Total profits after two years = profits for year 2015 – decreased amount in profits in year 2016.= Rs.77,040 – Rs.3,852= Rs. 73,188
Therefore, initially in year 2014, the profit was ${\text{Rs}}{\text{.72,000}}$ but after two years the profits were ${\text{Rs}}{\text{.73,188}}{\text{.}}$So, there is overall gain in profits.

Note: In this type of question, first calculate the increased amount in profits for the first successive year i.e.2015 and then calculate the total profits for the year 2015. Using the total profits of year 2015, calculate the decreased amount in profits for next year i.e. 2016. Finally to get total profits after two years subtract decreased amount in profits of year 2016 from total profits of year 2015. We can also use shortcut method to find total profits after two year which is given as:
Total profit after two year= profit for first year 2014$ \times \left( {1 + \dfrac{7}{{100}}} \right)\left( {1 - \dfrac{5}{{100}}} \right).$