Question : A man gives 50% of his money to his son and 30% to his daughter. 80% of the rest is donated to a trust. If he is left with Rs. 16,000 now, how much money did he have in the beginning?
Option 1: Rs. 40,000
Option 2: Rs. 8,00,000
Option 3: Rs. 80,000
Option 4: Rs. 4,00,000
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Correct Answer: Rs. 4,00,000
Solution : Let us assume the income of the man is Rs. $x$. According to the question, he gives 50% of his money to his son and 30% to his daughter. $\therefore$ The money he is left with = $x-\frac{x}{2}-\frac{3x}{10}$ $= \frac{10x-5x-3x}{10}$ $=\frac{2x}{10}=\frac{x}{5}$ According to the question, he donated 80% of the remaining money to the trust and the money left with him now is Rs. 16,000. ⇒ $\frac{x}{5}-\frac{80x}{5\times 100} = 16000$ ⇒ $\frac{x}{5}-\frac{8x}{50} = 16000$ ⇒ $\frac{10x-8x}{50}=16000$ ⇒ $2x=16000\times 50=8,00,000$ ⇒ $x=40,0000$ $\therefore$ The income of the man is Rs. 4,00,000. Hence, the correct answer is Rs. 4,00,000.
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