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) 4
(b) 40
(c) 14
(d) 45
The correct answers to the above question in:
Answer: (a)
S.I. = Rs.${2500 × 2 × 4}/100$ = Rs.200
C.I. = Rs.2500$[(1 + 4/100)^2 - 1]$
= Rs.2500$[(26/25)^2 - 1]$
= Rs.${(676 - 625)}/625$ × 2500
= Rs.$51/625 × 2500$ = Rs.204
The required difference
= C.I. - S.I. = Rs.(204 - 200) = Rs.4
Using Rule 6,
Here, C.I. - S.I.= ?, P = Rs.2500, R = 4%, T = 2
C.I. - S.I.= P$(R/100)^2$
= 2500$(4/100)^2$
= 2500 × $1/25 × 1/25$
C.I.–S.I. = Rs.4
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Read more difference in ci and si Based Quantitative Aptitude Questions and Answers
Question : 1
The difference between the simple and compound interest on a certain sum of money at 5% rate of interest per annum for 2 years is 15. Then the sum is :
a) 7,000
b) 6,500
c) 6,000
d) 5,500
Answer »Answer: (c)
Let the sum Rs.x. Then,
C.I. = $x(1 + 5/100)^2 - x$
= ${441x}/400 - x = {441x - 400x}/400$
= $41/400$x
Now, S.I. = ${x × 5 × 2}/100 = x/10$
(C.I.) - (S.I.)= ${41x}/400 - x/10$
= ${41x - 40x}/400 = x/400$
$x/400 = 15$
x = 15 × 400 = 6000
Hence, the sum is Rs.6000
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$(R/100)^2 × (3 + R/100)$
C.I. - S.I. = Rs.15, R = 5%, T = 2 years, P =?
C.I. - S.I. = P$(R/100)^2$
15 = P$(5/100)^2$
P = 15 × 400 = Rs.6000
Question : 2
If the difference between the simple and compound interests on a sum of money for 2 years at 4% per annum is 80, the sum is :
a) 1000
b) 5000
c) 10000
d) 50000
Answer »Answer: (d)
Using Rule 6,
When difference between the compound interest and simple interest on a certain sum of money for 2 years at r % rate is x, then the sum is given by
$x(100/r)^2$ Here x = Rs.80, r = 40%
Required sum = 80$(100/4)^2$
= 80 × 25 × 25 = Rs.50000
Question : 3
The difference between simple and compound interest (compounded annually) on a sum of money for 2 years at 10% per annum is 65. The sum is
a) 6500
b) 65650
c) 6565
d) 65065
Answer »Answer: (a)
Let the sum be x. Then,
C.I. = $x(1 + 10/100)^2 - x = {21x}/100$
S.I. = ${x × 10 × 2}/100 = x/5$
C.I. - S.I. = ${21x}/100 - x/5 = x/100$
Given that, $x/100$ = 65
x = 6500
Hence, the sum is Rs.6500.
Using Rule 6,
Here, C.I. - S.I. = Rs.65, R = 10%, T = 2 years, P = ?
C.I. - S.I. = P$(R/100)^2$
65 = P$(10/100)^2$ ⇒ P = Rs.6500
Question : 4
A sum of 6,000 is deposited for 3 years at 5% per annum compound interest (compounded annually). The difference of interests for 3 and 2 years will be
a) 375.00
b) 75.00
c) 330.75
d) 30.75
Answer »Answer: (c)
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$[(1 + r/100)^n - 1]$
C.I. after 3 years
= 6000$[(1 + 5/100)^3 - 1]$
= 6000$({9261 - 8000}/8000)$
= 6000 × $1261/8000$ = Rs.945.75
CI after 2 years
= $6000[(1 + 5/100)^2 - 1]$
= 6000$({441 - 400}/400)$
= 6000 × $41/400$ = Rs.615
Required difference
= Rs.(945.75 - 615) = Rs.330.75
Question : 5
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 : 6
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
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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