At simple interest, a sum doubles after 20 years. The rate of interest per…
2015
At simple interest, a sum doubles after 20 years. The rate of interest per annum is:
- A.
5%
- B.
10%
- C.
12%
- D.
Data inadequate
- E.
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Correct answer: A
Let the principal be P. Since the sum doubles, the amount after 20 years is 2P. Therefore, the simple interest (SI) is 2P - P = P.
Using the formula for simple interest: SI = (P × R × T) / 100, where R is the rate of interest per annum and T is time in years.
Substitute SI = P, T = 20 into the formula: P = (P × R × 20) / 100.
Simplify: 1 = (R × 20) / 100 → R = 100 / 20 = 5%.
Thus, the rate of interest per annum is 5%.
हिन्दी उत्तर:
माना मूलधन P है। चूँकि राशि 20 वर्षों में दोगुनी हो जाती है, अतः 20 वर्षों के बाद राशि 2P होगी। अतः साधारण ब्याज (SI) = 2P - P = P होगा।
साधारण ब्याज के सूत्र का उपयोग करने पर: SI = (P × R × T) / 100, जहाँ R वार्षिक ब्याज दर है और T वर्षों में समय है।
SI = P और T = 20 को सूत्र में रखने पर: P = (P × R × 20) / 100।
सरल करने पर: 1 = (R × 20) / 100 → R = 100 / 20 = 5%।
अतः वार्षिक ब्याज दर 5% है।