A man donated \(\frac{1}{10}\)th of his money to a school, \(\frac{1}{6}\)th of the remaining to an orphanage, and the remaining money he distributed equally among his three children. If each child gets ₹50000, how much money did the man originally have?
Answer (2)
To find out how much money the man originally had, we need to work backwards from the amount each child received.
Determine Money Received by Children :
Each child receives ₹50,000 and there are 3 children.
Total money distributed among children = 3 × ₹50,000 = ₹150,000.
Determine Remaining Money After Donations :
The money distributed to the children represents the remaining money after the man donated some to a school and an orphanage.
Calculate Money After Donation to Orphanage :
Let the amount of money he had after donating to the school be denoted as x .
He donated 6 1 th of this x amount to an orphanage.
So, remaining money after donation to orphanage = x − 6 1 x = 6 5 x .
This remaining money 6 5 x is equal to ₹150,000: 6 5 x = 150 , 000 Solving for x : x = 150 , 000 × 5 6 = 180 , 000
Calculate Original Total Money :
x = 180 , 000 is the amount of money left after donating to the school.
Since he donated 10 1 th of his original total money to the school:
Therefore, the original total money ( y ) is such that: y − 10 1 y = x = 180 , 000 10 9 y = 180 , 000 Solving for y : y = 180 , 000 × 9 10 = 200 , 000
Therefore, the man originally had ₹200,000.
The man originally had ₹200,000. He donated \frac{1}{10} of his money to a school and \frac{1}{6} of the remaining amount to an orphanage, with the rest distributed equally among his three children who received ₹50,000 each.
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