Solution
let use this formula to find the rate of interest that is
Amount=principal (1+$$\frac{r}{100})^t$$
Given data in the question is
Amount=8748
Principal=7500
Time=2years
Substitute above values in the formula then we will get
8748=7500(1+$$\frac{r}{100})^2$$
$$\frac{8748}{7500}$$=(1+$$\frac{r}{100})^2$$
Divide 8748 and 7500 by 12 then we get
$$\frac{729}{625}$$=(1+$$\frac{r}{100})^2$$
By eliminating square we get
$$\frac{27}{25}$$=(1+$$\frac{r}{100})$$
$$\frac{r}{100}$$=$$\frac{27}{25}$$-1
$$\frac{r}{100}$$=$$\frac{2}{25}$$
Rate of interest=$$\frac{100}{25}×2$$
Rate of interest=8
Therefore rate of compound interest=8%p.a
Now we have to find the simple interest for the sum ₹7500 for $$\frac{23}{5}$$ years at the rate=2×rate of interest
Rate of interest=2×8=16
Using the simple interest formula
Simple interest=$$\frac{principal×rate of interest ×time}{100}$$
Simple interest=$$\frac{7500×16×23}{5×100}$$
Simple interest=5520₹
Correct Answer - Option 2 : Rs. 3300
Given:
Principal = Rs. 7500
Amount = Rs. 8748
Time = 2 years
Concept used:
A = P × (1 + r/100)t
S.I = (P × R × T)/100
where A = amount, P = principal, R = rate of interest and t = time
Calculation:
7500 × (1 + r/100)2 = 8748
⇒ (1 + r/100)2 = 8748/7500 = 2916/2500
⇒ (1 + r/100)2 = (54/50)2
⇒ 1 + r/100 = 54/50
⇒ r/100 = (54/50) - 1 = 4/50
⇒ r = 8%
now,
according to the question,
P = Rs. 7500, r = 8 × 2.5 = 20% and time = 11/5 years
S.I = (7500 × 20 × 11/5)/100
⇒ (7500 × 4 × 11)/100 = 75 × 4 × 11
⇒ 300 × 11 = 3300
∴ The interest is Rs. 3300.
Correct Answer - Option 2 : 8%
Given:
Amount = Rs 8748
Principal = Rs 7500
Time = 2 years
Formula:
A = P(1 + R/100)n
Calculation:
A = P(1 + R/100)n
⇒ 8748 = 7500(1 + R/100)2
⇒ (1 + R/100)2 = 8748/7500
⇒ (1 + R/100)2 = 729/625
⇒ 1+ R/100 = 27/25
⇒ R/100 = 27/25 – 1
⇒ R/100 = 2/25
⇒ R = (2/25) × 100
⇒ R = 8%
∴ Rate of compound interest per annum is 8%
A sum of Rs. 7,500 amounts to Rs. 8,748 after 2 years at a certain rate per cent per annum compounded annually. What will be the simple interest for 3 years at double the earlier rate of interest?
This question was previously asked in
SSC MTS 2020 (Held On : 7 Oct 2021 Shift 2 ) Official Paper 8
View all SSC MTS Papers >
- 3,600
- 3,750
- 4,200
- 2,800
Answer (Detailed Solution Below)
Option 1 : 3,600
Free
CT : GK (Ancient History)
10 Questions 10 Marks 6 Mins
Given
Principal = Rs.7500
Amount = Rs 8748
Time = 2 years
Formula used
A = P(1 + r%)t
Simple interest = prt/100
Interest = Amount - Principal
where A, p, r, t are Amount, principal, rate and time respectively
Calculation
8748 = 7500(1 + r%)2
⇒ 8748/7500 = (1 + r/100)2
⇒ 8748/7500 = (100 + r)2/(100)2
⇒ (8748 × 100 × 100)/7500 = (100 + r)2
⇒ 11664 = (100 + r)2
⇒ √ 11664 = 100 + r
⇒ 108 = 100 + r
⇒ 108 - 100 = r
⇒ 8 = r
rate is double = 2(8)
⇒16
Simple interest = (7500 × 16 × 3)/100
⇒ 3600
∴ The simple interest on Rs.7500 for 3 years at double the earlier rate is Rs.3600.
Last updated on Oct 27, 2022
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