Question

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. What amount of money did Mr. Jones have initially?

• A. \rupee 1,00,000
• B. \rupee 1,50,000
• C. \rupee 75,000
• D. \rupee 1,25,000

Hint:

When solving such percentage problems, break the problem down step-by-step, calculating the remaining amounts after each transaction. Keep track of how much is spent and what remains, and use simple equations to solve for the unknown amount.

Answer 1

The Correct Option is A

Step 1: Let the initial amount of money Mr. Jones had be \( x \).
He gave 40\% of the money to his wife, so the amount given to his wife is: \[ \text{Amount to wife} = 0.4x \] The remaining amount after giving money to his wife is: \[ \text{Remaining amount} = x - 0.4x = 0.6x \] Step 2: Mr. Jones gave 20\% of the remaining amount to each of his three sons.
For each son, the amount given is: \[ \text{Amount given to each son} = 0.2 \times 0.6x = 0.12x \] Since there are three sons, the total amount given to the sons is: \[ \text{Total amount to sons} = 3 \times 0.12x = 0.36x \] After giving money to his sons, the remaining amount is: \[ \text{Remaining amount after sons} = 0.6x - 0.36x = 0.24x \] Step 3: Half of the remaining amount was spent on miscellaneous items.
The amount spent on miscellaneous items is: \[ \text{Amount spent} = 0.5 \times 0.24x = 0.12x \] After spending on miscellaneous items, the remaining amount is: \[ \text{Remaining amount after spending} = 0.24x - 0.12x = 0.12x \] Step 4: The remaining amount of ¥ 12,000 was deposited in the bank.
So, we have: \[ 0.12x = 12,000 \] Step 5: Solving for \( x \): \[ x = \frac{12,000}{0.12} = 100,000 \] Thus, Mr. Jones initially had \rupee 1,00,000. Answer: \rupee 1,00,000