Question:
A sum of money becomes 4 times itself in 15 years at simple interest. In how many years will it become 7 times itself at the same rate?
कोई धनराशि साधारण ब्याज पर 15 वर्षों में स्वयं की 4 गुनी हो जाती है। उसी दर से कितने वर्षों में यह स्वयं की 7 गुनी हो जाएगी?
Options:
- 25 years
- 30 years
- 35 years
- 40 years
- 25 वर्ष
- 30 वर्ष
- 35 वर्ष
- 40 वर्ष
Correct Answer: b)
Explanation:
In simple interest, becoming 4 times means interest earned is \(4P – P = 3P\).
Time taken to earn \(3P\) interest = 15 years.
Rate of earning interest = \(\dfrac{3P}{15} = \dfrac{P}{5}\) per year.
To become 7 times, interest needed = \(7P – P = 6P\).
\(\text{Time} = \dfrac{6P}{P / 5} = 6 \times 5 = 30\text{ years}\).
साधारण ब्याज में 4 गुना होने का अर्थ है अर्जित ब्याज \(4P – P = 3P\) है।
\(3P\) ब्याज में लगा समय = 15 वर्ष।
प्रति वर्ष ब्याज = \(\dfrac{3P}{15} = \dfrac{P}{5}\)।
7 गुना होने के लिए आवश्यक ब्याज = \(7P – P = 6P\)।
समय = \(6 \times 5 = 30\text{ वर्ष}\)।