type 4 difference & equality of si rate & years Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on simple interest topic of quantitative aptitude
(a) 6%
(b) 10%
(c) 9%
(d) 8%
The correct answers to the above question in:
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
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Read more difference equality in si rate years Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
The simple interest on a certain sum for 8 months at 4% per annum is Rs.129 less than the simple interest on the same sum for 15 months at 5% per annum. The sum is :
a) Rs.2400
b) Rs.2,580
c) Rs.3600
d) Rs.2529
Answer »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
Question : 3
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 : 4
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 = $√{100/16} = 10/4 = 2{1}/2%$
Question : 5
If x, y, z are three sum of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then we have
a) $xyz$ = 1
b) $z^2 = xy$
c) $y^2 = zx$
d) $x^2 = yz$
Answer »Answer: (c)
Using Rule 1,
S.I. = ${P × R × T}/100$
$y = {x × T × R}/100$
and $z = {y × T × R}/100$
So, $y/z = x/y = ⇒ y^2 = zx$
Question : 6
The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by Rs.42. The sum is :
a) Rs.280
b) Rs.210
c) Rs.840
d) Rs.750
Answer »Answer: (c)
According to question,
Interest of one year = Rs.42
Rate = 5% and Time = 1 year
Principal = $\text"Interest × 100"/\text"Rate × Time"$
= ${42 × 100}/{5 × 1}$ = Rs.840
Using Rule 13The difference between the S.I. for a certain sum $P_1$ deposited for time $T_1$ at $R_1$ rate of interest and another sum $P_2$ deposited for time $T_2$ at $R_2$ rate of interest isS.I. = ${P_2R_2T_2 - P_1R_1T_1}/100$
$P_1 = P, R_1 = 5%, T_1$ = 3years.
$P_2 = P, R_2 = 5%, T_2$ = 4 years.
S.I.= 42
42 = ${20P - 15P}/100$
P = 42 × 20 = Rs.840
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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