Question : Deepak started a business with a capital of INR 1,60,000. He incurs a loss of 10% 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 25% on his new capital during the third year. Find his total profit at the end of three years.
Option 1: INR 29,500
Option 2: INR 29,000
Option 3: INR 28,000
Option 4: INR 28,500
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Correct Answer: INR 29,000
Solution :
Initial capital, $P$ = INR. 1,60,000
Loss for the first year, $a$ = 10%
Gain for the second year, $b$ = 5%
Gain for the third year, $c$ = 25%
Hence, capital after 3 years, $Q = P(1-\frac{a}{100})(1+\frac{b}{100})(1+\frac{c}{100})$
⇒ $Q= P(1-\frac{10}{100})(1+\frac{5}{100})(1+\frac{25}{100})$
⇒ $Q=160000(\frac{90}{100})(\frac{105}{100})(\frac{125}{100})$
⇒ $Q=189000$
So, total profit = 189000 – 160000 = INR. 29,000
Hence, the correct answer is INR 29,000.
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