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) 3075
(b) 6150
(c) 4612.5
(d) 7687.5
The correct answers to the above question in:
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
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Read more combination of si and ci Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
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 %
Question : 4
The simple interest on a sum of money at 4% per annum for 2 years is Rs.80. The compound interest in the same sum for the same period is
a) Rs.81.60
b) Rs.82.60
c) Rs.81.80
d) Rs.82.20
Answer »Answer: (a)
Principal = $\text"S.I. × 100"/ \text"Time × Rate"$
= ${80 × 100}/{2 × 4}$ = Rs.1000
C.I. = P$[(1 + R/100)^T - 1]$
= 1000$[(1 + 4/100)^2 - 1]$
= 1000$[(25/26)^2 - 1]$
= 1000$(676/625 - 1)$
= 1000$({676 - 625}/625)$
= ${1000 × 51}/625$= Rs.81.60
Using Rule 10,
Here, S.I. = Rs.80, R = 4%, C.I. = ?
C.I.= S.I.$(1 + R/200)$
C.I.= 80$(1 + 4/200)$
= $80(1 + 1/50)$
= 80 × $51/50$ = Rs.81.60
Question : 5
A man borrowed some money from a private organisation at 5% simple interest per annum. He lended 50% of this money to another person at 10% compound interest per annum and thereby the man made a profit of Rs.3,205 in 4 years. The man borrowed.
a) Rs.1,50,000
b) Rs.80,000
c) Rs.1,20,000
d) Rs.1,00,000
Answer »Answer: (d)
Using Rule 1,
Sum borrowed = Rs.x
Simple interest after 4 years
= ${x × 4 × 5}/100$ = Rs.$x/5$
Amount lent of on compound interest = Rs.$x/2$
C.I. = P$[(1 + R/100)^T - 1]$
= $x/2[(1 + 10/100)^4 - 1]$
= $x/2[(1.1)^4 - 1]$
= $x/2$ (1.4641 - 1) = Rs.${0.4641x}/2$
${0.4641x}/2 - x/5$ = 3205
${2.3205x - 2x}/10$ = 3205
0.3205x = 32050
$x = 32050/{0.3205}$ = Rs.100000
Question : 6
If the compound interest on a certain sum for two years at 12% per annum is Rs.2,544, the simple interest on it at the same rate for 2 years will be
a) Rs.2,440
b) Rs.2,400
c) Rs.2,480
d) Rs.2,500
Answer »Answer: (b)
C.I. = P$[(1 + R/100)^T - 1]$
2544 = P$[(1 + 12/100)^2 - 1]$
2544 = P$[(28/25)^2 - 1]$
2544 = P$(784/625 - 1)$
2544 = P$({784 - 625}/625)$
2544 = ${P × 159}/625$
P = ${2544 × 625}/159$ = Rs.10000
S.I. = ${P × R × T}/100$
= ${10000 × 2 × 12}/100$ = Rs.2400
Using Rule 10,
Here, C.I. = Rs.2544, R = 12%, S.I. = ?
C.I. = S.I.$(1 + R/200)$
2544 = S.I.$(1 + 12/200)$
2544 = S.I.$(212/200)$
S.I. = ${2544 × 200}/212$ = Rs.2400
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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