model 4 difference in ci & si Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on compound interest topic of quantitative aptitude
(a) 28,000
(b) 40,000
(c) 32,000
(d) 36,000
The correct answers to the above question in:
Answer: (c)
Using Rule 6,
Time = $3/2 × 2 = 3$ half years
Rate = $10/2$ = 5% per half year
[Since, when r → $r/2$, then t → 2t]
Difference = P$(r^3/1000000 + {3r^2}/10000)$
244 = P$(125/1000000 + 75/10000)$
244 = P$(7625/1000000)$
P = ${244 × 1000000}/7625$ = Rs.32000
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Read more difference in ci and si Based Quantitative Aptitude Questions and Answers
Question : 1
The difference between the compound and the simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually, is 28. If the interest were compounded halfyearly, the difference in the two interests will be
a) 43.29
b) 44
c) 43.41
d) 28.35
Answer »Answer: (c)
Using Rule 6,The difference between C.I. and S.I. on a sum 'P' in 2 years at the rate of R% rate of compound interest will beC.I - S.I. = P$(R/100)^2 = {S.I. × R}/200$ For 3 years, C.I. - S.I. = P$(R/100)^2 × (3 + R/100)$
Using Rule 1,If A = Amount, P = Principal, r = Rate of Compound Interest (C.I.), n = no. of years then,A=P$(1 + r/100)^n$, C.I. = A - PC.I. = P$[(1 + r/100)^n - 1]$
If the difference between compound interest and simple interest at the rate of r% per annum for 2 years be x, then
Principal = $x(100/r)^2$
= 28$(100/10)^2$ = Rs.2800
If the interest is compounded half yearly, then
r = $10/2$ = 5%,
Time = 4 half years
Simple interest
= ${2800 × 5 × 4}/100$ = Rs.560
Compound interest
= $2800[(1 + 5/100)^4 - 1]$
= 2800 [1.2155 - 1]
= 2800 × 0.2155 = 603.41
Difference = Rs.(603.41–560) = Rs.43.41
Question : 2
On a certain sum of money lent out at 16% p.a. the difference between the compound interest for 1 year, payable half yearly, and the simple interest for 1 year is 56. The sum is
a) 5780
b) 1080
c) 8750
d) 7805
Answer »Answer: (c)
Using Rule 6,
Rate of interest = 8% per halfyear
Time = 2 half years
Difference of interests = ${PR^2}/100$
56 = $P × (8)^2/(100)^2$
P = ${56 × 10000}/64$ = 8750
Question : 3
The difference between simple and compound interest on a certain sum of money for 2 years at 4 per cent per annum is 1. The sum of money is :
a) 650
b) 600
c) 560
d) 625
Answer »Answer: (d)
Using Rule 6,
When difference between the CI and SI on a certain sum of money for 2 years at r % rate is x, then
Sum = x × $(100/r)^2$
= 1 × $(100/4)^2$ = Rs.625
Question : 4
If the difference between S.I. and C.I. for 2 years on a sum of money lent at 5% is 6, then the sum is
a) 2000
b) 2200
c) 2600
d) 2400
Answer »Answer: (d)
Using Rule 6,The difference between C.I. and S.I. on a sum 'P' in 2 years at the rate of R% rate of compound interest will beC.I - S.I. = P$(R/100)^2 = {S.I. × R}/200$ For 3 years, C.I. - S.I. = P$(R/100)^2 × (3 + R/100)$
Difference = ${Pr^2}/10000$
6 = ${P × 5 × 5}/10000$
P = 6 × 400 = Rs.2400
Question : 5
Find the difference between the compound interest and the simple interest on 32,000 at 10% p.a. for 4 years.
a) 2501.20
b) 2051.20
c) 2025.20
d) 2052.50
Answer »Answer: (b)
Using Rule 1,
S.I. = $\text"Principal × Time × Rate"/100$
= ${32000 × 4 × 10}/100$ = Rs.12800
C.I. = P$[(1 + R/100)^4 - 1]$
= 32000$[(1 + 10/100)^4 - 1]$
= 32000 $[(1.1)^4$ - 1]
= 32000 (1.4641 - 1)
= 32000 × 0.4641= Rs.14851.2
Required difference
= 14851.2 - 12800 = Rs.2051.2
Question : 6
The difference between simple and compound interest compounded annually, on a certain sum of money for 2 years at 4% per annum is 1. The sum (in ) is :
a) 640
b) 650
c) 625
d) 630
Answer »Answer: (c)
Using Rule 6,
The difference between compound interest and simple interest for two years
= ${\text"Principal" × (Rate)^2}/{100 × 100}$
1 = ${\text"Principal" × (4)^2}/10000$
Principal = $10000/16$ = Rs.625
compound interest Shortcuts and Techniques with Examples
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model 1 basic compound interest using formula
Defination & Shortcuts … -
model 2 at ci sum becomes ‘n’ times after ‘t’ years
Defination & Shortcuts … -
model 3 combination of si & ci
Defination & Shortcuts … -
model 4 difference in ci & si
Defination & Shortcuts … -
model 5 ci with instalments
Defination & Shortcuts … -
model 6 comparing sum in different years
Defination & Shortcuts …
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