type 4 difference & equality of si rate & years Practice Questions Answers Test with Solutions & More Shortcuts

Question : 1 [SSC CGL Tier-I 2015]

Ram deposited a certain sum of money in a company at 12% per annum simple interest for 4 years and deposited equal amount in fixed deposit in a bank for 5 years at 15% per annum simple interest. If the difference in the interest from two sources is Rs.1350, then the sum deposited in each case is :

a) Rs.4000

b) Rs.3000

c) Rs.6500

d) Rs.5000

Answer: (d)

Let amount invested in each company be Rs. x.

S.I. = ${\text"Principal × Rate × Time"/100$

According to the question,

${x × 15 × 5}/100 - {x × 12 × 4}/100$ = 1350

${75x}/100 - {48x}/100$ = 1350

${27x}/100$ = 1350

$x = {1350 × 100}/27$ = Rs. 5000

Using Rule 13

Here, $P_1 = Rs. P, R_1 = 12%, T_1$ = 4 years

$P_2 = Rs. P, R_2 = 15%, T_2$ = 5 years

S.I. = Rs. 1350

S.I.= ${P_2R_2T_2 - P_1R_1T_1}/100$

1350 = ${P × 15 × 5 - P × 12 × 4}/100$

135000 = 75 P - 48P

135000 = 75 P

P = Rs. 5000

Question : 2 [SSC CGL Tier-I 2011]

Simple interest on a certain sum at a certain annual rate of interest is $16/25$ of the sum. If the number representing rate per cent and time in years be equal, then the rate of interest is

a) 11$1/2$%

b) 8%

c) 12$1/4$%

d) 12$1/2$%

Answer: (b)

Let the rate of interest be r% and principal be P.

According to the question.

${16P}/25 = {P × r × r}/100$

[Since, r = t numerically]

$r^2 = 1600/25$

r = $40/5$ = 8 %

Using Rule 5
If Simple Interest (S.I.) becomes 'n' times of principal i.e.
S.I. = P × n then.
RT = n × 100

Here, n = $16/25$, R = T

Now R × R = $16/25$ × 100

$R^2 = 1600/25$

R = $√{1600/25} = 40/5$ = 8%

Question : 3 [SSC CGL Tier-II 2014]

Prakash lends a part of Rs.20,000 at 8% simple interest and remaining at $4/3$% simple interest. His total income after a year was Rs.800. Find the sum lent at 8%.

a) Rs.12,000

b) Rs.8,000

c) Rs.10,000

d) Rs.6,000

Answer: (b)

Using Rule 1,

Amount lent at 8% rate of interest = Rs.x

Amount lent at $4/3$% rate of interest = Rs.(20,000 - x)

S.I. = ${\text"Principal × Rate × Time"/100$

${x × 8 × 1}/100 + {(20,000 - x) × 4/3 × 1}/100$ = 800

${2x}/25 + {20,000 - x}/75 = 800$

${6x + 20,000 - x}/75 = 800$

5x + 20,000 = 75 × 800 = 60,000

5x = 60,000-20,000 = 40,000

$x = {40,000}/5$ = Rs.8000

Question : 4 [SSC Delhi Police S.I.2012]

The rate of interest per annum at which the total simple interest of a certain capital for 1 year is equal to the total simple interest of the same capital at the rate of 5% per annum for 2 years, is

a) 10%

b) $5/2$%

c) 12.5%

d) 25%

Answer: (a)

Using Rule 1
Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ or
S.I. = ${\text"P × R × T"/100$
P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$
A = P + S.I. or S.I. = A - P

${P × r × 1}/100 = {P × 5 × 2}/100$

[Since,Capital is same in both cases]

r × 1 = 5 × 2 = 10%

Question : 5 [SSC CGL Prelim 2000]

The simple interest on a sum of money is $4/9$ of the principal and the number of years is equal to the rate percent per annum. The rate per annum is :

a) 6$2/3$%

b) 5%

c) 7$1/5$%

d) 6%

Answer: (a)

Using Rule 1
Simple Interest (S.I.)= ${\text"Principal × Rate × Time"/100$ or
S.I. = ${\text"P × R × T"/100$
P = ${\text"S.I." × 100}/\text"R × T"$, R = ${\text"S.I." × 100}/\text"P × T"$, T = ${\text"S.I." × 100}/\text"P × R"$
A = P + S.I. or S.I. = A - P

We know that

S.I. = $\text"PRT"/100$

According to question,

S.I.= $4/9P$ & R = T (numerically)

$4/9P = {P × R × R}/100$

$R^2 = 400/9$

R = $√{400/9} = 20/3 = 6{2}/3$%

IMPORTANT quantitative aptitude EXERCISES

type 4 difference & equality of si rate & years Shortcuts »

Click to Read...

type 4 difference & equality of si rate & years Online Quiz

Click to Start..

Recently Added Subject & Categories For All Competitive Exams

New 100+ Compound Interest MCQ with Answers PDF for IBPS

Compound Interest verbal ability questions and answers solutions with PDF for IBPS RRB PO. Aptitude Objective MCQ Practice Exercises all competitive exams

02-Jul-2024 by Careericons

Continue Reading »

100+ Mixture and Alligation MCQ Questions PDF for IBPS

Most importantly Mixture and Alligation multiple choice questions and answers with PDF for IBPS RRB PO. Aptitude MCQ Practice Exercises all Bank Exams

02-Jul-2024 by Careericons

Continue Reading »

IBPS Profit and Loss Questions Solved Problems with PDF

Most important Profit and Loss multiple choice questions and answers with PDF for IBPS RRB PO. 100+ Aptitude MCQ Practice Exercises all competitive exams

28-Jun-2024 by Careericons

Continue Reading »

100+ Average Aptitude Questions Answers solutions MCQ PDF

New Average multiple choice questions and answers with PDF for IBPS RRB PO. 100+ Quantitative Aptitude MCQ Practice Exercises all competitive exams

28-Jun-2024 by Careericons

Continue Reading »