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A man borrowed some money from a private organisation at 5% simple interest per annum. He lended 50% of this money to another person at 10% compound interest per annum and thereby the man made a profit of Rs. 3,205 in 4 years. The man borrowed.
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- Rs. 80,000
- Rs. 1,00,000
- Rs. 1,20,000
- Rs. 1,50,000
Correct Option: B
Suppose Sum borrowed = Rs. P
Given that , Rate ( R ) = 5% , Time = 4 years
∴ Simple interest after 4 years ( SI ) = | = Rs. | ||
100 | 5 |
Amount lent of on compound interest = Rs. | |
2 |
∴ C.I. = P | ![]() | ![]() | 1 + | ![]() | T | − 1 | ![]() | |
100 |
C.I. = | ![]() | ![]() | 1 + | ![]() | 4 | − 1 | ![]() | ||
2 | 100 |
C.I. = | [(1.1)4 − 1] | |
2 |
C.I. = | (1.4641 − 1) | |
2 |
C.I. = Rs. | |
2 |
∴ C.I. - S.I. = 3205
∴ | − | = 3205 | ||
2 | 5 |
⇒ | = 3205 | |
10 |
⇒ 0.3205P = 32050
⇒ P = | = Rs. 100000 | |
0.3205 |