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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