Mr. Jones gave 40% of the money he had, to his wife. He also gave 20% of the remaining amount to each of his… · ABC26GN2126
Subject: General Aptitude · Chapter: Percentage
Mr. Jones gave 40% of the money he had, to his wife. He also gave 20% of the remaining amount to each of his three sons. Half of the amount now left was spent on miscellaneous items and the remaining amount of ` 12,000 was deposited in the bank. How much money did Mr. Jones have initially?
Answer
No answer key was printed for this question.
Explanation
Let the initial amount with Mr. Jones be ₹ $x$. Then, money given to wife $=₹\frac{40}{100}x=₹\frac{2x}{5}$. Balance $=₹\left(x-\frac{2x}{5}\right)=₹\frac{3x}{5}$. Money given to 3 sons $=₹\left[3\times\left(\frac{20}{100}\times\frac{3x}{5}\right)\right]=₹\frac{9x}{25}$. Balance $=₹\left(\frac{3x}{5}-\frac{9x}{25}\right)=₹\frac{6x}{25}$. Amount deposited in bank $=₹\left(\frac{1}{2}\times\frac{6x}{25}\right)=₹\frac{3x}{25}$. $\frac{3x}{25}=12000 \Leftrightarrow x=\left(\frac{12000\times 25}{3}\right)=100000$. So, Mr. Jones initially had ₹1,00,000 with him. Short-cut Method: $\frac{1}{2}$ of $[100-(3\times 20)]\%$ of $(100-40)\%$ of $x=12000 \Leftrightarrow \frac{1}{2}\times\frac{40}{100}\times\frac{60}{100}\times x=12000 \Leftrightarrow \frac{3}{25}x=12000 \Leftrightarrow x=100000$.
Explanation as extracted from the printed page; notation may be imperfect.