(i) Here,
I = Rs 2356.25
R =7 \frac{1}{4} \% \text { p.a }
= 29 / 4 % p.a.
T = 2 \frac{1}{2} \text { years }
= 5 / 2 years
Hence,
P = (I × 100) / (R × T)
= Rs (2356.25 × 100) / (29 / 4) × (5 / 2)
On further calculation, we get,
= Rs (2356.25 × 100 × 4 × 2) / (29 × 5)
= Rs (235625 × 8) / (29 × 5)
We get,
= Rs (47125 × 8) / 29
= Rs 1625 × 8
= Rs 13000
(ii) Amount (A) = Rs 11300
Rate (R) = 4% p.a.
Time (T) = 3 years 3 months
=3 \frac{3}{12} \text { years }
=\frac{3}{4} \text { years }
= 13 / 4 years
Let the principal be Rs x
Hence,
S.I. = (P × R × T) / 100
= Rs (x × 4 × 13) / (100 × 4)
We get,
= Rs 13x / 100
Then,
Amount = Principal + Simple Interest
= Rs x + Rs 13x / 100
= Rs (x + 13x) / 100
We get,
= Rs (100x + 13x) / 100
= Rs (113x / 100)
But, the amount given is Rs 11300
Hence,
113x / 100 = 11300
x = 11300 × 100 / 113
x = 100 × 100
We get,
x = 10000
Therefore, principal (P) = Rs 10000
A sum of money becomes 137.5% of itself in 6 years at a certain rate of interest. Then what will be rate of interest?
- 12.25%
- 6.25%
- 7.25%
- 11.25%
Answer (Detailed Solution Below)
Option 2 : 6.25%
Free
10 Questions 10 Marks 7 Mins
Given:
In 6 years a sum becomes 137.5% of itself
Formula used:
S. I. = (P × t × r)/100
S. I = Simple Interest
P = principal
t = Time period
r = Rate of interest
Calculation:
Let P is the original amount.
After 6 years, it becomes 137.5% of P.
⇒ New amount = (137.5/100)P = 11/8P
⇒ Inntrest = 11P/8 - P = 3P/8
Now using the above formula, let the rate of interest be R.
⇒ 3P/8 = (P × 6 × R)/100
⇒ 1/8 = R/50
∴ R = 6.25 %
Alternate MethodLet the P be 8x
137.5% = 11/8
8x × 11/8 = 11x
According to the question,
Interest = 11x – 8x = 3x
3x = (8x × 6 × r)/100
⇒ 300x = 48xr
⇒ 25 = 4r
⇒ 25/4 = r
⇒ r = 6.25
⇒ Rate of interest = 6.25%
∴ The rate of interest is 6.25%
Alternate Method
In 6 years 8P becomes 11P
Interest = 11P – 8P = 3P
3P in 6 years
⇒ 0.5P in 1 year
Rate % = (0.5P/8P) × 100
⇒ 0.0625 × 100
⇒ 6.25%
⇒ Rate of interest = 6.25%
∴ The rate of interest is 6.25%
Last updated on Sep 21, 2022
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The compound interest on a sum of money at 5% per annum for a period of 2 years is ₹ 6560. What will be the simple interest on the same sum for the same period at the same rate?
- ₹ 6400
- ₹ 6440
- ₹ 6260
- ₹ 6380
Answer (Detailed Solution Below)
Option 1 : ₹ 6400
Free
Rajasthan - History and Culture : Part 1
12 Questions 15 Marks 10 Mins
Given:
Time = 2 years
Rate, R = 5% per annum
CI = ₹ 6560
Concept:
- \(CI= P[(1+\frac{R}{100})^n-1]\)
SI = (PRT)/100
Calculation:
We know that,
\(CI= P[(1+\frac{R}{100})^n-1]\)
\(⇒ 6560= P[(1 + \frac{5}{100})^2-1]\)
⇒ 6560 = P[(21/20)2 - 1]
⇒ 6560 = P[(441/400) - 1]
⇒ 6560 = P(41/400)
⇒ P = 64000
Now, SI = (64000 × 5 × 2)/100
⇒ SI = 6400
Hence, the simple interest is ₹ 6400.
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