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
Answer (as printed):
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.