Question

John got a prize of ₹75000 in a TV contest. He paid 1/10 of the prize as income tax. Out of the remaining, he gave 1/3 to his son, 1/5 to his daughter, 1/10 to the Red Cross Society, and the rest to his wife. What portion of the prize did John's wife get and how much?

Answer 1

Given :

Total price won in contest : ₹75000

Part of price paid to income tax : ⅒

Part of money given to son : ⅓

Part of money given to daughter : ⅕

Part of money to Red cross society : ⅒

Remaining money was given to his wife.

To find :

The total money given to the wife.

Solution :

First, we should find the money given to each of them.

Money paid to income tax :

$\sf \dashrightarrow \dfrac{1}{10} \: of \: 75000$

$\sf \dashrightarrow \dfrac{1}{10} \times 75000$

$\sf \dashrightarrow \dfrac{1 \times 75000}{10}$

$\sf \dashrightarrow \cancel \dfrac{75000}{10} = 7500$

Money remaining with John :

$\sf \dashrightarrow 75000 - 7500$

$\sf \dashrightarrow Rs.67500$

Now, let's find the money given to his son, daughter and society.

Money given to son :

$\sf \dashrightarrow \dfrac{1}{3} \: of \: 67500$

$\sf \dashrightarrow \dfrac{1}{3} \times 67500$

$\sf \dashrightarrow \dfrac{1 \times 67500}{3}$

$\sf \dashrightarrow \cancel \dfrac{67500}{3} = 22500$

Remaining money :

$\sf \dashrightarrow 67500 - 22500$

$\sf \dashrightarrow Rs.45000$

Money given to daughter :

$\sf \dashrightarrow \dfrac{1}{5} \: of \: 45000$

$\sf \dashrightarrow \dfrac{1}{5} \times 45000$

$\sf \dashrightarrow \dfrac{1 \times 45000}{5}$

$\sf \dashrightarrow \cancel \dfrac{45000}{5} = 9000$

Remaining money :

$\sf \dashrightarrow 45000 - 9000$

$\sf \dashrightarrow Rs.36000$

Money given to Red cross society :

$\sf \dashrightarrow \dfrac{1}{10} \: of \: 36000$

$\sf \dashrightarrow \dfrac{1}{10} \times 36000$

$\sf \dashrightarrow \dfrac{1 \times 36000}{10}$

$\sf \dashrightarrow \cancel \dfrac{36000}{10} = 3600$

Remaining money :

$\sf \dashrightarrow 36000 - 3600$

$\sf \dashrightarrow Rs.32400$

Now, let's find the money given to his wife.

Total money given to wife :

$\sf \dashrightarrow 75000 - 32400$

$\sf \dashrightarrow Rs.42600$

Part of money given to his wife :

$\sf \dashrightarrow \dfrac{42600}{75000} \times 100$

$\sf \dashrightarrow \dfrac{426}{750} \times 100$

$\sf \dashrightarrow \dfrac{436}{75} \times 10$

$\sf \dashrightarrow \dfrac{436 \times 10}{75} = \dfrac{4360}{75}$

$\sf \dashrightarrow \cancel \dfrac{4360}{75} = \dfrac{872}{15}$

Hence, the total money given to her wife is ₹42600 and $\sf \dfrac{872}{15}$.