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A sum of money becomes eight times in 3 years, if the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times?
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- 6 years
- 4 years
- 8 years
- 5 years
Correct Option: B
Given that , Time = 3 years , Rate = R%
Let the principal be ₹ 1 and Amount = ₹ 8
| ∴ A = P |  | 1 + |  | T | |
| 100 |
| ⇒ 8 = 1 | | 1 + | | 3 | |
| 100 |
| ⇒ 23 = 1 | | 1 + | | 3 | |
| 100 |
| ⇒ 2 = | | 1 + | | 1 | |
| 100 |
| ⇒ 24 = | | 1 + | | 4 | |
| 100 |
∴ Time = 4 years
We can find required answer with the help of given formula :
Here, p = 8, n1 = 3 and q = 16, n2 = ?
Using p1/n1 = q1/n2
(8)1/3 = (16)1/n2
(23)1/3 = (24)1/n2
21 = 24/n2
| ⇒ 1 = | |
| n2 |
∴ n2 = 4 years
