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

Questions : 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

The correct answers to the above question in:

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

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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$1/2$% 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: (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 : 2

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: (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 : 3

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: (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 - P
C.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 : 4

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: (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 : 5

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: (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 - P
C.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 : 6

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: (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

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GET compound interest PRACTICE TEST EXERCISES

model 1 basic compound interest using formula

model 2 at ci sum becomes ‘n’ times after ‘t’ years

model 3 combination of si & ci

model 4 difference in ci & si

model 5 ci with instalments

model 6 comparing sum in different years
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