model 5 ci with instalments Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CGL Prelim 2000]

A builder borrows Rs.2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be ?

a) Rs.1283

b) Rs.1352

c) Rs.1275

d) Rs.1377

Answer: (b)

A = Rs.2550

R = 4% per annum

n = 2 years

Let each of the two equal instalments be x

Present worth = $\text"Instalment"/(1 + r/100)^n$

$P_1 = x/(1 + 4/100)^1 = x/{1 + 1/25} = x/{26/25}$

or $P_1 = 25/26x$

Similarly,

$P_2 = (25/26)^2x = 625/676x$

$P_1 + P_2$ = A

$25/26x + 625/676x$ = 2550

${(650 + 625)x}/676 = 2550$

$1275/676x = 2550$

x = 2550 $× 676/1275$ ⇒ x = Rs.1352

Using Rule 9,
If a sum 'P' is borrowed at r% annual compound interest which is to be paid in 'n' equal annual installments including interest, then
(i) For n = 2, Each annual installment
= $p/{(100/{100 + r}) + (100/{100 + r})^2$
(ii) For n = 3, Each annual installment
= $p/{(100/{100 + r}) + (100/{100 + r})^2 + (100/{100 + r})^3$

Here, P = Rs.2550, n = 2, r = 4%

Each instalment

= $p/{(100/{100 + r}) + (100/{100 + r})^2$

= $2550/{(100/{100 + 4}) + (100/{100 + 4})^2$

= $2550/{100/104 + (100/104)^2}$

= $2550/{100/104(1 + 100/104)}$

= $2550/{100/104 (204/104)}$

= ${2550 × 104 × 104}/20400 $= Rs.1352

Question : 2 [SSC CGL Prelim 2008]

Kamal took Rs.6800 as a loan which along with interest is to be repaid in two equal annual instalments. If the rate of interest is 12$1/2$%, compounded annually, then the value of each instalment is

a) Rs.4000

b) Rs.8100

c) Rs.4050

d) Rs.4150

Answer: (c)

Let the annual instalment be x

A = P$(1 + R/T)^T$

$x = P_1(1 + 25/200)$

$x = P_1 × 9/8$

$P_1 = 8/9x$

Similarly, $P_2 = 64/81x$

$P_1 + P_2$ = 6800

$8/9x + 64/81x$ = 6800

${72x + 64x}/81 = 6800$

${136x}/81 = 6800$

$x = {6800 × 81}/136$ = Rs.4050

Using Rule 9(i),

Here, P = Rs.6800, R = $25/2$%, n = 2

Each instalment

= $p/{(100/{100 + r}) + (100/{100 + r})^2$

= $6800/{(100/{100 +{25/2}}) + (100/{100 + {25/2}})^2$

= $6800/{200/225 + (200/225)^2}$

= $6800/{200/225(1 + {200/225})}$

= ${6800 × 225 × 225}/{200 × 425}$ = Rs.4050

Question : 3 [SSC CHSL 2014]

A sum of Rs.210 was taken as a loan. This is to be paid back in two equal instalments. If the rate of interest be 10% compounded annually, then the value of each instalment is

a) Rs.225

b) Rs.127

c) Rs.210

d) Rs.121

Answer: (d)

Using Rule 9(i),

Let the value of each instalment be Rs.x

Principal = Present worth of Rs.x due 1 year hence, present worth of Rs. x due 2 years hence

210 = $x/(1 + R/100) + x/(1 + R/100)^2$

210 = $x/(1 + 10/100) + x/(1 + 10/100)^2$

210 = $x/{1 + 1/10} + x/(1 + 1/10)^2$

210 = $x/{11/10} + x/(11/10)^2$

210 = ${10x}/11 + {100x}/121$

210 = ${110x + 100x}/121$

210 × 121 = 210 x

$x = {210 × 121}/210$ = Rs.121

Question : 4 [SSC CHSL 2015]

Mr. Dutta desired to deposit his retirement benefit of Rs. 3 lakhs partly to a post office and partly to a bank at 10% and 6% interests respectively. If his monthly interest income was Rs. 2000, then the difference of his deposits in the post office and in the bank was :

a) Rs.1,00,000

b) Rs.50,000

c) Nil

d) Rs.40,000

Answer: (c)

Using Rule 1,

Let the amount deposited in Post Office be Rs.x lakhs.

Amount deposited in bank = Rs.(3 - x) lakhs

According to the question,

${x × 10 × 1}/{100 × 12} + {(3 - x) × 6 × 1}/{100 × 12}$

= $2000/100000 = 1/50$

10x + 18 - 6x

= $1/50$ × 1200 = 24

4x = 24 - 18 = 6

x = $6/4$ = Rs.$3/2$ lakhs

∴ Required difference = 0

Question : 5 [SSC CHSL 2015]

The income of a company increases 20% per year. If the income is Rs. 26,64,000 in the year 2012, then its income in the year 2010 was :

a) Rs.21,20,000

b) Rs.28,55,000

c) Rs.28,20,000

d) Rs.18,50,000

Answer: (d)

Using Rule 1,

Let the income of company in 2010 be Rs.P

According to the question,

A = P$(1 + R/100)^T$

2664000 = P$(1 + 20/100)^2$

2664000 = P$(1 + 1/5)^2$

2664000 = P × $(6/5)^2$

P = ${2664000 × 5 × 5}/{6 × 6}$ = Rs.1850000

IMPORTANT quantitative aptitude EXERCISES

model 5 ci with instalments Shortcuts »

Click to Read...

model 5 ci with instalments Online Quiz

Click to Start..

Recently Added Subject & Categories For All Competitive Exams

Number System - Aptitude Problems For IBPS RRB PO Prelims

Free Important 100+ Aptitude Number System practice multiple choice questions and answers test & Quiz PDF for IBPS RRB PO (Officer Scale 1) Prelims 2024 Exam

29-Mar-2024 by Careericons

Continue Reading »

Classification MCQ Test: IBPS RRB PO 2024 Scale-1 Prelims

Free 150+ Classification Verbal Reasoning Multiple choice questions and answers practice test series PDF, Free Quiz For IBPS RRB PO Officer Scale 1 Level 2024

28-Mar-2024 by Careericons

Continue Reading »

100+ Analogy Verbal Questions Answers PDF For IBPS RRB PO

Most Important Analogy Verbal Reasoning Multiple choice questions and answers practice test series PDF & Free Quiz For IBPS RRB PO Officer Scale 1 Level 2024

27-Mar-2024 by Careericons

Continue Reading »

IBPS RRB Clerk 2024 Seating Arrangement Questions Answers

Seating Arrangement: Verbal Reasoning Practice multiple choice questions and answers test & Quiz PDF for IBPS RRB (Assistant Multipurpose) Clerk Prelims 2024

26-Mar-2024 by Careericons

Continue Reading »