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) 10%
(b) 4%
(c) 8%
(d) 6%
The correct answers to the above question in:
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 %
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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 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 : 2
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 : 3
If the compound interest on a sum for 2 years at 12$1/2$% per annum is Rs.510, the simple interest on the same sum at the same rate for the same period of time is :
a) Rs.460
b) Rs.400
c) Rs.450
d) Rs.480
Answer »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
Question : 4
A certain amount of money earns Rs.540 as Simple Interest in 3 years. If it earns a Compound Interest of Rs.376.20 at the same rate of interest in 2 years, find the amount (in Rupees).
a) 2100
b) 1600
c) 2000
d) 1800
Answer »Answer: (c)
S.I. for 2 years
= $2/3$ × 540 = Rs.360
C.I. - S.I.
= 376.20 - 360 = Rs.16.20
Rate of interest
= ${16.20}/180$ × 100 = 9% per annum
Principal = $\text"S.I. × 100"/\text"Time × Rate"$
= ${180 × 100}/{1 × 9}$ = Rs.2000
Question : 5
On a certain sum of money the compound interest for 2 years is Rs.282.15 and the simple interest for the same period of time is Rs.270. The rate of interest per annum is
a) 12.15%
b) 6.07%
c) 9%
d) 10%
Answer »Answer: (c)
Using Rule 10,
If SI on a certain sum for two years is x and CI is y, then
$y = x(r + /200)$
$282.15 = 270(1 + r/100)$
$1 + r/200 = 282.15/270$
$r/200 = 282.15/270$ - 1
$r/200 = {12.15}/270$
r = ${12.15 × 200}/270 = 9%$
Question : 6
There is 40% increase in an amount in 8 years at simple interest. What will be the compound interest (in rupees) of Rs 30000 after 2 years at the same rate ?
a) 3075
b) 6150
c) 4612.5
d) 7687.5
Answer »Answer: (a)
According to the question,
If principal
= Rs.100 then interest = Rs.40.
Case I.
Rate = $\text"S.I. × 100"/ \text"Principal × Time"$
= ${40 × 100}/{100 × 8}$ = 5% per annum
Case II.
A = P$(1 + R/100)^T$
= 30000$(1 + 5/100)^2$
= 30000$(1 + 1/20)^2$
= 30000$({20 + 1}/20)^2$
= 30000$ × 21/20 × 21/20$
= Rs.33075
C. I. = Rs.(33075 - 30000) = Rs.3075
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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