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Varun gave 60% of the money he had to his wife. He also gave 20% of the remaining amount to each of his three children. Three-fifth of the amount now left was spent on miscellaneous items, and the remaining amount of Rs. 9,600 was deposited in the bank. How much money did Varun have initially?

Varun gave 60% of the money he had to his wife. He also gave 20% of the remaining amount to each of his three children. Three-fifth of the amount now left was spent on miscellaneous items, and the remaining amount of Rs. 9,600 was deposited in the bank. How much money did Varun have initially? Correct Answer Rs. 1,50,000

Given

Amount given to wife = 60% of total money

Amount given to three children each = 20% of money left after giving to wife

Amount spent on miscellaneous items = (3/5)th of the money left after giving to wife and children

Amount deposited = 9600

Concept

Total money = sum of the money given to wife , children, spent on miscellaneous items and deposited in bank

Calculation

let the total money is Rs.x

amount given to wife = 60% of x

⇒60x/100

Money left after given to wife = x - 60% of x

⇒40x/100

Amount given to three children = 3 × (40x/100) × 20%

⇒(120x/100) × (20/100)

⇒24x/100

Amount left for miscellaneous items = x -

⇒x - (84x/100)

⇒(100x - 84x)/100

⇒16x/100

Amount spent on miscellaneous items = (3/5) × (16x/100)

⇒48x/500

According to question

(60x/100) + (24x/100) + (48x/500) + 9600 = x

⇒(84x/100) + (48x/500) + 9600 = x

⇒ + 9600 = x

⇒ + 9600 = x

⇒9600 = x - (468x/500)

⇒9600 = (500x - 468x)/500

⇒9600 = 32x/500

⇒(9600 × 500)/32 = x

⇒300 × 500 = x

⇒150000 = x

∴ Initial amount Varun has is RS.1,50,000.

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