type 4 difference & equality of si rate & years Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 6 EXERCISES
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The following question based on simple interest topic of quantitative aptitude
(a) Rs.2400
(b) Rs.2,580
(c) Rs.3600
(d) Rs.2529
The correct answers to the above question in:
Answer: (c)
Let the sum be x
${x × 5 × 15}/{100 × 12} - {x × 4 × 8}/{100 × 12}$ = 129
$x/{100 × 12}$(75 - 32) = 129
$x = {129 × 1200}/43$ = Rs.3600
Using Rule 13,
$P_1 = P, R_1 = 4%$
$T_1 = 8 months = 8/12$ years
$P_2 = P, R_2$ = 5%
$T_2 = 15 month = 15/12$ years
S.I. = Rs.129
129 = ${P × 5 × 15/12 - P × {4 × 8}/12}/100$
12900 = ${75P - 32P}/12$
12900 = ${43P}/12$
P = Rs.3600
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Read more difference equality in si rate years Based Quantitative Aptitude Questions and Answers
Question : 1
The difference between the simple interest received from two different sources on Rs.1500 for 3 years is Rs.13.50. The difference between their rates of interest is:
a) 0.2%
b) 0.1%
c) 0.4%
d) 0.3%
Answer »Answer: (d)
Let $r_1$, and $r_2$ be the required rate of interest
Then, ${13.50} = {1500 × 3 × r_1}/100$
– ${1500 × 3 × r_2}/100 = 4500/100(r_1 - r_2)$
$r_1 - r_2 = 135/450 = 27/90$
= $3/10$ = 0.3%
Using Rule 13,
$P_1 = Rs.1500, R_1 , T_1$ = 3 years.
$P_2 = Rs.1500, R_2 , T_2$ = 3 years.
S.I. = Rs.13.50
13.50 = ${1500 × R_2 × 3 - 1500 × R_1 × 3}/100$
$1350/100 = {4500(R_2 - R_1)}/100$
$R_2 - R_1 = 1350/4500 = 27/90$
= $3/10$ = 0.3%
Question : 2
The simple interest on a sum of money is $1/9$ of the principal and the number of years is equal to rate per cent per annum. The rate per annum is
a) $1/3$%
b) 3%
c) $3/10$%
d) 3$1/3$%
Answer »Answer: (d)
$\text"Simple interest"/ \text"Principal" = 1/9$
If the annual rate of interest be r%, then
Rate = $\text"S.I. × 100"/ \text"Principal × Time"$
$r = 1/9 × 100/r$
$r^2 = 100/9$
r = $√{100/9} = 10/3 = 3{1}/3$%
Using Rule 5,
Here, n = $1/9$, R = T
RT = n × 100
$R^2 = 1/9 × 100 = 100/9$
R = $√{100/9} = 10/3 = 3{1}/3$%
Question : 3
The simple interest on a sum of money is $1/4$th of the principal and the number of years is equal to rate per cent per annum. The rate per cent is
a) 5%
b) 2.5%
c) 10%
d) 7.5%
Answer »Answer: (a)
Let the principal be x and rate be y% per annum.
According to the question,
SI = ${P × R × T}/100$
$x/4 = {x × y × y}/100$
$y^2 = 100/4$ = 25
y = $√{25}$ = 5% per annum
Using Rule 5,
n = $1/5$, R = T
RT = n × 100
$R^2 = 1/4 × 100$ = 25
R = 5%
Question : 4
A borrows Rs.800 at the rate of 12% per annum simple interest and B borrows Rs.910 at the rate of 10% per annum, simple interest. In how many years will their amounts of debt be equal ?
a) 20 years
b) 18 years
c) 24 years
d) 22 years
Answer »Answer: (d)
Using Rule 1,
Let the period of time be T years.
800 + ${800 × 12 × T}/100$
= 910 + ${910 × 10 × T}/100$
800 + 96 T = 910 + 91T
96 T - 91 T = 910 - 800
5T = 110
T = $110/5$ = 22 years.
Question : 5
The simple interest on Rs.4,000 in 3 years at the rate of x% per annum equals the simple interest on Rs.5,000 at the rate of 12% per annum in 2 years. The value of x is
a) 6%
b) 10%
c) 9%
d) 8%
Answer »Answer: (b)
Using Rule 1,
S.I. = ${\text"Principal × Rate × Time"/100$
${4000 × 3 × x}/100$
= ${5000 × 2 × 12}/100$
$x = {5 × 2 × 12}/{4 × 3}$
= 10% per annum
Question : 6
The simple interest on a sum of money is $1/16$ of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is
a) 2$1/2$%
b) 1$1/2$%
c) 4$1/2$%
d) 3$1/2$%
Answer »Answer: (a)
Let the annual rate of interest = r%
Time = r years
Let the principal be x .
Interest = $x/16$
According to the question,
$x/16 = {x × r × r}/100$ [Since, r = t]
16$r^2$ = 100
$r^2 = 100/16 = 25/4$
r = $√ {25/4} = 5/2 = 2{1}/2$%
Using Rule 5,
Here, n = $1/16$, R = T
RT = n × 100
$R^2 = 100/16$
R = $√{100/16} = 10/4 = 2{1}/2%$
simple interest Shortcuts and Techniques with Examples
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type 1 basic simple interest using formula
Defination & Shortcuts … -
type 2 increase or decrease in interest rate
Defination & Shortcuts … -
type 3 money multiples in ‘n’ years
Defination & Shortcuts … -
type 4 difference & equality of si rate & years
Defination & Shortcuts … -
type 5 si on ‘n’ years & ‘x/y ‘of sum
Defination & Shortcuts … -
type 6 si with ratios
Defination & Shortcuts …
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