model 3 combination of si & ci 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) Rs.460
(b) Rs.400
(c) Rs.450
(d) Rs.480
The correct answers to the above question in:
Answer: (d)
C.I. = P$[(1 + R/100)^T - 1]$
510 = P$[(1 + 25/200)^2 - 1]$
510 = P$(81/64 - 1)$
P = ${510 × 64}/17$ = 1920
S.I. = ${1920 × 2 × 25}/{100 × 2}$ = Rs.480
Using Rule 10,
Here, C.I. = Rs.510, R = 12$1/2$%, S.I. = ?
C.I. = S.I.$(1 + R/200)$
$510 = S.I.(1 + 25/400)$
S.I. = ${510 × 400}/425$ = Rs.480
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Read more combination of si and ci Based Quantitative Aptitude Questions and Answers
Question : 1
If the compound interest on a sum for 2 years at 12$1/2$ p.a is Rs.510, the simple interest on the same sum at the same rate for the same period of time is
a) Rs.480
b) Rs.400
c) Rs.460
d) Rs.450
Answer »Answer: (a)
Principal = Rs.P (let)
C.I. = P$[(1 + R/100)^T - 1]$
510 = P$[(1 + 25/200)^2 - 1]$
510 = P$[(1 + 1/8)^2 - 1]$
510 = P$[(9/8)^2 - 1]$
510 = P$(81/64 - 1)$
510 = P$({81 - 64}/64)$
510 = ${17P}/64$
P = ${510 × 64}/17$ = Rs.1920
S.I. = $\text"Principal × Time × Rate"/100$
= ${1920 × 2 × 25}/{100 × 2}$ = Rs.480
Using Rule 10,
Here, C.I. = Rs.510, R = 12$1/2$%, S.I. = ?
C.I. = S.I.$(1 + R/200)$
510 = S.I.$(1 + 25/400)$
510 = S.I.$(425/400)$
S.I. = ${510 × 400}/425$ = Rs.480
Question : 2
If the compound interest on a sum of money for 3 years at the rate of 5% per annum is Rs.252.20, the simple interest on the same sum at the same rate and for the same time is
a) Rs.250
b) Rs.220
c) Rs.245
d) Rs.240
Answer »Answer: (d)
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$[(1 + r/100)^n - 1]$
Suppose principal be x
$x((1 + 5/100)^3 - 1) = 252.20$
$x((21/20)^3 - 1)$ = 252.20
$x({21 × 21 × 21 - 20 × 20 × 20}/{20 × 20 × 20})$ = 252.20
$x 1261/8000$ = 252.20
x = ${252.20 × 8000}/1261$ = 1600
SI = ${1600 × 5 × 3}/100$ = Rs.240
Question : 3
On a certain sum of money, the simple interest for 2 years is Rs.350 at the rate of 4% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned ?
a) Rs.35
b) Rs.3.50
c) Rs.14
d) Rs.7
Answer »Answer: (d)
Principal = $\text"S.I. × 100"/\text"Time × Rate"$
= ${350 × 100}/{2 × 4}$ = Rs.4375
Difference = ${PR^2}/10000$
= ${4375 × 4 × 4}/10000$ = Rs.7
Question : 4
A sum becomes Rs.2,916 in 2 years at 8% per annum compound interest. The simple interest at 9% per annum for 3 years on the same amount will be
a) Rs.625
b) Rs.600
c) Rs.650
d) Rs.675
Answer »Answer: (d)
Using Rule 1,
A = P$(1 + R/100)^T$
2916 = $x(1 + 8/100)^2$
2916 = $x(27/25)^2$
$x = {2916 × 25 × 25}/{27 × 27}$ = Rs.2500
S.I. = ${P × R × T}/100$
= ${2500 × 9 × 3}/100$ = Rs.675
Question : 5
If the compound interest on a certain sum for 2 years at 4% p.a. is Rs.102, the simple interest at the same rate of interest for two years would be
a) Rs.100
b) Rs.200
c) Rs.150
d) Rs.50
Answer »Answer: (a)
If the sum be P, then
C.I. = P$[(1 + R/100)^T - 1]$
102 = $[(1 + 4/100)^2 - 1]$
102 = P$[(26/25)^2 - 1]$
102 = P$(676/625 - 1)$
102 = P$({676 - 625}/625)$
102 = P × $51/625$
P = ${102 × 625}/51$ = Rs.1250
S.I. = ${1250 × 2 × 4}/100$ = Rs.100
Question : 6
At a certain rate per annum, the simple interest on a sum of money for one year is Rs.260 and the compound interest on the same sum for two years is Rs.540.80. The rate of interest per annum is
a) 10%
b) 4%
c) 8%
d) 6%
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$[(1 + r/100)^n - 1]$
Let the principal be x and rate of interest be r% per annum. Now,
S.I. = $\text"Principal × Time × Rate"/100$
260 = ${x × r}/100$ ....(i)
C.I.= P$[(1 + R/100)^T - 1]$
540.80 = $x[(1 + r/100)^2 - 1]$
540.80 = $x[1 + {2r}/100 + r^2/10000 - 1]$
540.80 = ${2xr}/100 + {xr^2}/10000$
540.80 = 2 × 260 + ${260 . r}/100$
260r = 54080 - 52000
260r = 2080
r = $2080/260$ = 8 %
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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