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) 2$1/2$%
(b) 1$1/2$%
(c) 4$1/2$%
(d) 3$1/2$%
The correct answers to the above question in:
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 = $√{100/16} = 10/4 = 2{1}/2%$
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Read more difference equality in si rate years Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
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 : 4
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 : 5
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
Question : 6
If Rs.12,000 is divided into two parts such that the simple interest on the first part for 3 years at 12% per annum is equal to the simple interest on the second part for 4$1/2$ years at 16% per annum, the greater part is
a) Rs.6,000
b) Rs.8,000
c) Rs.7,500
d) Rs.7,000
Answer »Answer: (b)
Using Rule 1,
Let the larger part of the sum be x
Smaller part = Rs.(12000 - x)
According to the question,
${x × 3 × 12}/100 = {(12000 - x) × 9 × 16}/{2 × 100}$
36 x = (12000 - x ) 72
x = (12000 - x ) × 2
x + 2x = 24000
3x = 24000
$x = 24000/3$ = Rs.8000
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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