A sum becomes 2.5 times of itself in 5 years under simple interest. In how many years will it become 5 times itself at the same rate?
\(13\tfrac{1}{3}\) years
Use the simple-interest relation \(A = P + \dfrac{P R T}{100}\).
Step 1 — find the rate from the first condition.
Sum becomes 2.5P in 5 years, so \(SI = 2.5P - P = 1.5P\).
\(1.5P = \dfrac{P \cdot R \cdot 5}{100} \;\Longrightarrow\; R = \dfrac{1.5 \times 100}{5} = 30\%\text{ per annum}\)
Step 2 — find the time for the sum to become 5P at the same rate.
Now \(SI = 5P - P = 4P\).
\(4P = \dfrac{P \cdot 30 \cdot T}{100} \;\Longrightarrow\; T = \dfrac{4 \times 100}{30} = \dfrac{40}{3} = 13\tfrac{1}{3}\text{ years}\)
Hence the time is \(13\tfrac{1}{3}\) years — option (2).
Similar Questions
- If the simple interest on a sum of Rs. A at 6% per annum for 2 years is equal to the simple interest on Rs. B at 4% per annum for 3 years, then what is the ratio of A to B?
- A sum doubles in 5 years at simple interest. What is the annual rate?
- A certain sum becomes 4 times itself in 8 years at simple interest. In how many years will it become 12 times itself at the same rate?
- If the simple interest on a certain sum of money for 4 years at 5% per annum is ₹500, what would be the simple interest on the same sum for 6 years at 7% per annum?
- If $P = \text{Rs. } 1500$, $R = 8.5\%$, and $T = 2.5 \text{ years}$, find the simple interest.
- A donor deposits ₹8,00,000 in a trust that earns 10% simple interest annually. The interest is used to distribute three annual awards. If the second and third awards are ₹35,000 and ₹20,000 respectively, what is the value of the first award?
- Rs. $1500$ is lent out at $6\%$ per annum simple interest for $3$ years. Find the amount after $3$ years.
- A sum amounts to ₹6,600 in 2 years and ₹7,200 in 4 years at simple interest. What is the rate of interest per annum?
A sum of ₹8000 is lent out in two parts, one at 5% simple interest and the other at 7% simple interest. If the annual interest is ₹500, the sum lent at 7% is:
What will the ratio be of the simple interest earned on a given amount at the same interest rate over 6 years compared to that earned over 9 years?
Important Questions from Simple Interest
If ₹12,800 is invested in a bank for 5 years at the rate of 9% per annum simple interest. what amount is returned by the bank?
Somu has borrowed ₹10,000 from a money lender with simple interest at a rate of 7% half yearly. How much amount will he pay to the money lender after 3 years?
Find the Simple interest on Rs. 2,400 from 20 March 2019 to 31 may 2019 at \(6{1 \over 4}\) % rate?
If the simple interest for five years is equal is 35% of the principal, that rate of interest is:
A sum fetched a simple interest of Rs. 3,040 at the rate of 8% p.a in 5 years. what is the sum?
