Pranav gave 30% of the money he had to his wife, and 86% of the remaining to his two children. Half of the amount left was spent on other things, and the remaining amount of ₹98,000 was deposited in the bank. How much money did he have initially?

Given:

Pranav gave 30% of the money he had to his wife, and 86% of the remaining to his two children. Half of the amount left was spent on other things, and the remaining amount of ₹98,000 was deposited in the bank.

Formula used:

Let the initial amount be ₹X.

After giving 30% to his wife, he has 70% of X left.

Then, he gives 86% of the remaining to his children, so he is left with 14% of 70% of X.

Half of the remaining amount is spent on other things, and the final amount left is ₹98,000.

Calculation:

Amount after giving to wife = 70% of X = 0.7X

Amount after giving to children = 14% of 0.7X = 0.14 × 0.7X

⇒ Remaining amount = 0.14 × 0.7X = 0.098X

Half of the remaining amount is spent, so the amount left is 0.098X / 2 = 0.049X

Given this amount is ₹98,000, we set up the equation:

0.049X = 98,000

⇒ X = 98,000 / 0.049

⇒ X = 20,00,000

∴ The correct answer is option (4).