A man embarks his whole capital upon 4 successive ventures. On the first he gains 100% and on each of the remaining three he loses at the rate of 20%. Find out the percentage gain on his original capital.
Answers
Given :- A man embarks his whole capital upon 4 successive ventures. On the first he gains 100% and on each of the remaining three he loses at the rate of 20%. Find out the percentage gain on his original capital. ?
Solution :-
Let us assume that, Total capital of man was Rs.100 .
we know that,
when amount is given in successive ventures , then,
- Capital In the end = capital before * {1 + (gain%/100)}^(No. ot times.)
- if Loss is given we using subtraction in bracket .
given that,
- Gains = 100% .
- Loss = 20% = 3 times.
So,
→ Capital in the end = 100 * {1 + (100/100)} * {1 - (20/100)}³
→ Capital in the end = 100 * (1 + 1) * {1 - (1/5)}³
→ Capital in the end = 200 * (4/5)³
→ Capital in the end = (200 * 64) / 125
→ Capital in the end = Rs.102.4 .
Therefore,
→ Total gain in his capital = 102.4 - 100 = Rs.2.4
Hence,
→ Total gain in his capital = (2.4 * 100) / 100 = 2.4% (Ans.)
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