Two years ago, arthur gave each of his five children 20% of his fortune to invest in any way they saw fit. in the first year, three of the children, alice, bob, and carol, each earned a profit of 50% on their investments, while two of the children, dave and errol, lost 40% on their investments. in the second year, alice and bob each earned a 10% profit, carol lost 60%, dave earned 25% in profit, and errol lost all the money he had remaining. what percentage of arthur's fortune currently remains?
Answers
Answer: Arthur has the 93% of his investment remaining
Explanation: There are five children of Arthur, whom he distributed 20% of his wealth to each child.
Let the total wealth of Arthur be Rs. 100
1. Alice: Rs. 100 × 20% = Rs. 20
2. BOB: Rs. 100 × 20% = Rs. 20
3. Carol: Rs. 100 × 20% = Rs. 20
4. Dave: Rs. 100 × 20% = Rs. 20
5. Errol: Rs. 100 × 20% = Rs. 20
Now, in Year 1, the profit earned by each of them:
1. Alice: Rs. 20 × 50% = Rs. 10
2. BOB: Rs. 20 × 50% = Rs. 10
3. Carol: Rs. 20 × 50% = Rs. 10
4. Dave: Rs. 20 × -40% = -Rs. 8
5. Errol: Rs. 20 × -40% = -Rs. 8
Now, in Year 2, the total investment is
1. Alice: Rs. 20 + Rs. 10 = Rs. 30
2. BOB: Rs. 20 + Rs. 10 = Rs. 30
3. Carol: Rs. 20 + Rs. 10 = Rs. 30
4. Dave: Rs. 20 - Rs. 8 = Rs. 12
5. Errol: Rs. 20 - Rs. 8 = Rs. 12
Now the above amount is reinvested in Year 2:
1. Alice: Rs. 30 × (1+ 10%) = Rs. 33
2. BOB: Rs. 30 × (1+ 10%) = Rs. 33
3. Carol: Rs. 30 × ( 1 - 60%) = Rs. 12
4. Dave: Rs. 12 × (1 - 25%) = Rs. 15
5. Errol: Rs. 12 × -100% = Rs. 0
The total investment of Arthur will be the sum of the investment value at the end of year 2 of all the children:
Rs. 33 + Rs. 33 + Rs. 12 + Rs. 15 + Rs. 0
Total Investment of Arthur = Rs. 93