A person has some amount initially. He gives 30% of the amount to his wife. Then from the remaining amount, he gives 20%, 20% and 15%, respectively, to both his sons and one daughter. Now from the amount left, he pays $$\frac13$$​of the amount as house rent and the remaining amount of ₹33,600 he deposits in the bank. Find his initial amount.

Correct option is C

Given:

Person gives the part of amount to his wife =30%

He then gives amount of 20% ,20% and 15% to his ons and daughters

One-third of amount is given as house rent

Rest amount of ₹33600 is deposited in bank

Formula Used:

Percentage

Solution:

let the amount initially be x

Then amount given to wife = 30% of x =0.3x

Amount left = x -0.3x =0.7x

Then amount of 20%, 20% and 15% is given from the remaining amount

Total amount given = 20+20+15 =55%

= 55% of 0.7x = 0.385x

Amount left = 0.7x -0.385x = 0.315x

One-third of remaining amount is given as house rent = $$\frac{1}{3} \times 0.315x =0.105x$$​​

Amount left = 0.315x -0.105x = 0.21x

But 0.21x = ₹33600

​$$x= \frac{33600}{0.21}= 1,60,000$$​​

Alternative Method:

​$$33600 =Initial \ amount \times \frac{100-30}{100} \times \frac{100-55}{100} \times \frac{2}{3}$$​​

​$$Initial \ amount = 33600 \times \frac{100}{70} \times \frac{100}{45} \times \frac{3}{2}$$​​

= ₹1,60,000