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.287
(b) Rs.320
(c) Rs.300
(d) Rs.308
The correct answers to the above question in:
Answer: (b)
Let the principal be P.
C.I. = P$[(1 + R/100)^T - 1]$
328 = P$[(1 + 5/100)^2 - 1]$
328 = P$[441/400 -1]$
328 = P$[{441 - 400}/400]$
P = ${328 × 400}/41$ = Rs.3200
S.I. = ${PRT}/100 = {3200 × 5 × 2}/100$ = Rs.320
Using Rule 10,
Here, C.I. = Rs.328, R = 5%, S.I. = ?
C.I.= S.I.$(1 + R/200)$
328 = S.I.$(1 + 5/200)$
328 = S.I.$(1 + 1/40)$
S.I. = ${328 × 40}/41$
S.I. = 8 x 40 = Rs.320
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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 3% per annum is Rs.101.50, then the simple interest on the same sum at the same rate and for the same time will be
a) Rs.98.25
b) Rs.90.00
c) Rs.100.00
d) Rs.95.50
Answer »Answer: (c)
Let the sum be P.
101.50 = P$[(1 + 3/100)^2 - 1]$
[Since, C.I. = P$[(1 + r/100)^n - 1]$]
101.50 = P$[(103/100)^2 - 1]$
=P$({10609 - 10000}/10000)$
P = Rs.${101.50 × 10000}/609 = Rs.1015000/609$
S.I. = ${1015000 × 2 × 3}/{609 × 100}$ = Rs.100
Using Rule 10,The simple interest for a certain sum for 2 years at an annual rate interest R% is S.I., thenC.I. = S.I.$(1 + R/200)$
Here, C.I. = Rs.101.50, R = 3%, S.I. = ?
C.I. = S.I.$(1 + R/200)$
101.50 = S.I.$(1 + 3/200)$
S.I. = ${101.50 × 200}/203$ = Rs.100
Question : 2
There is 100% increase to an amount in 8 years, at simple interest. Find the compound interest of Rs.8000 after 2 years at the same rate of interest.
a) Rs.2125
b) Rs.2500
c) Rs.2250
d) Rs.2000
Answer »Answer: (a)
Using Rule 1,
Let S.I. = Rs.100, & Principal = Rs.100
Rate = $\text"S.I. × 100"/\text"Principal × Time"$
= ${100 × 100}/{100 × 8} = 25/2$%
C.I. = P$[(1 + r/100)^T - 1]$
= 8000$[(1 + 25/200)^2 - 1]$
= 8000 $(81/64 - 1)$
= ${8000 × 17}/64$ = Rs.2125
Question : 3
The simple interest on a certain sum of money for 2 years at 5% is Rs.1600. The compound interest at the same rate after 3 years interest compound annually, is
a) Rs.2535
b) Rs.2520
c) Rs.2555
d) Rs.2522
Answer »Answer: (d)
Principal = $\text"S.I. × 100"/\text"Time × Rate"$
= ${1600 × 100}/{5 × 2}$ = Rs.16000
C.I. = P$[(1 + R/100)^T - 1]$
= 16000$[(1 + 5/100)^3 –1]$
= 16000$[(21/20)^3 - 1]$
= $16000(9261/8000 - 1)$
= ${16000 × 1261}/8000$ = Rs.2522
Question : 4
The compound interest on a certain sum of money at a certain rate per annum for two years is Rs.2,050, and the simple interest on the same amount of money at the same rate for 3 years is Rs.3, 000. Then the sum of money is
a) Rs.25, 000
b) Rs.20,000
c) Rs.21,000
d) Rs.18,000
Answer »Answer: (b)
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$(R/100)^2 × (3 + R/100)$
S.I. for 3 years = Rs.3000
S.I. for 2 years = $3000/3 × 2$ = Rs.2000
C.I. - S.I. = 2050 - 2000 = Rs.50
S.I. = ${PR × 3}/100$
PR = ${3000 × 100}/3$ = Rs.100000
Difference = ${P × R^2}/10000$
50 = ${P × (100000)^2}/{10000 × P^2}$
P = $1000000/50$ = Rs.20000
Question : 5
The compound interest on a certain sum of money at a certain rate for 2 years is Rs.40.80 and the simple interest on the same sum is Rs.40 at the same rate and for the same time. The rate of interest is
a) 5% per annum
b) 2% per annum
c) 4% per annum
d) 3% per annum
Answer »Answer: (c)
Let the principal be P and rate of interest be r per cent per annum. Then,
C. I = P$[(1 + r/100)^2 - 1]$
40.80 = P$[(1 + r/100)^2 - 1]$...(i)
S.I. = ${P.r.t}/100 ⇒ 40 = {Pr × 2}/100$ ...(ii)
${40.80}/40 = P[(1 + r/100)^2 - 1]/{{2Pr}/100}$ ⇒ 1.02
= $100/{2r}[1 + r^2/10000 + {2r}/100 - 1]$
1.02 = $r/200$ +1
$r/200$ = 1.02 - 1
r = 0.02 × 200 = 4% per annum.
Using Rule 10,
Here, C.I. = Rs.40.80, S.I. = Rs.40, R = ?
C.I.= S.I.$(1 + R/200)$
40.80 = 40$(1 + R/200)$
$4080/4000 = 1 + R/200$
$408/400 = {200 + R}/200$
408 = 400 + 2R
2R = 8 ⇒ R = 4%
Question : 6
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
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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