A man starts a business with a capital of Rs $1000000$ . He incurs a loss of $4 %$ during the first year. But he makes a profit of $5 %$ during the second year on his remaining investment. Finally, he makes a profit of $10 %$ on his new capital during the third year. Find his total profit at the end of three years.

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Solution

Here, initial capital $P = 1000000$ ,
loss for the first year $= r_{1} % = 4 %$ ,
gain for the second year $= r_{2} % = 5 %$ and
gain for the third year $= r_{3} % = 10 %$
$Q = P (1 - \frac{r_{1}}{100}) (1 + \frac{r_{2}}{100}) (1 + \frac{r_{3}}{100})$
$\Rightarrow Q = 1000000 (1 - \frac{4}{100}) (1 + \frac{5}{100}) (1 + \frac{10}{100})$
$∴, Q = 1000000 \times \frac{24}{25} \times \frac{21}{20} \times \frac{11}{10}$
$\Rightarrow Q = 200 \times 24 \times 21 \times 11$
$\Rightarrow Q = 1108800$
$∴,$ profit at the end of three years $= 1108800 - 1000000 = 108800$

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