Given :
Principal $P = Rs. 4500$
Amount $A = Rs. 5715$
Time $T = 3$ years
To do :
We have to find the rate of interest.
Solution :
Let the rate percent be R.
We know that,
$Amount (A) = Principal (P) + Simple Interest (SI)$
$Simple Interest (SI) = Amount (A) - Principal (P)$
$= Rs. (5715 - 4500)$
$= Rs. 1215$
$SI = \frac{PRT}{100}$
Therefore,
$Rs. 1215 = \frac{(4500 \times R \times 3)}{100}$
$Rs. 1215 = 45 \times R \times 3$
$R = \frac{1215}{(45\times3)}$
$R = 9$
The rate percent is 9%.
A certain sum at 20% per annum simple interest becomes Rs. 3600 in 3 years. In how many years the principle becomes Rs. 4500 at the same rate of interest?
- 4 years
- 5 years
- 6 years
- 7 years
Answer (Detailed Solution Below)
Option 2 : 5 years
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150 Questions 150 Marks 150 Mins
Given:
Rate = 20%
Amount = Rs. 3600 and T = 3 years
Concept:
Simple interest is the interest calculated on the principal portion of the loan or the original contribution to the saving account.
Formula Used:
Simple Interest = (P × R × T)/100
Amount = Principal + Interest
Calculation:
Let the principal be 'P'
⇒ Simple interest = 3600 - P
⇒ 3600 - P = (P × 20 × 3)/100
⇒ 3600 - P = 3P/5
⇒ 18000 - 5P = 3P
⇒ 8P = 18000
⇒ P = 18000 ÷ 8 = 2250
Now, When P = Rs. 2250, amount = Rs. 4500 and rate = 20%
Simple interest = 4500 - 2250 = Rs. 2250
Let time be T
⇒ 2250 = (2250 × 20 × T)/100
⇒ T = 5 years
∴ The time is 5 years in which principle become Rs. 4500 at 5%.
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Let's discuss the concepts related to Interest and Simple Interest. Explore more from Quantitative Aptitude here. Learn now!
At what rate of interest will a sum of Rs. 4500 amounts to Rs. 6525 at simple interest for 5 years ?
- 9%
- 5%
- 10%
- 11%
Answer (Detailed Solution Below)
Option 1 : 9%
Given:
Principal = Rs. 4500
Amount = Rs. 6525
Time = 5 years
Concept used:
Simple interest
Calculation:
\({\rm{si = }}\frac{{{\rm{P}} \times {\rm{R}} \times {\rm{T}}}}{{100}}\)
Principal + interest = Amount
Interest = Amount - Principal
Interest = 6525 - 4500 = 2025
Interest for 5 years = Rs. 2025
Interest for 1 year = 2025/5 = Rs. 405
\({\rm{Rate = }}\frac{{{\rm{Interest}}\; \times \;{\rm{100}}}}{{{\rm{Principal}}\; \times \;{\rm{Time}}}}\)
Rate = \(\frac{{405\; \times \;100}}{{4500}} = 9\% \)
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