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) 30 years
(b) 20 years
(c) 22 years
(d) 10 years
The correct answers to the above question in:
Answer: (b)
Let the principal be P and rate of interest be r %
According to the question,
${30P}/100 = {P × R × 6}/100$
30 = 6 R
R = 5
Now, let interest be equal to principal in T years.
P = ${P × 5 × T}/100$
T = $100/5$ = 20 years.
Using Rule 5,
Here, n = $30/100 = 3/10$, T = 6 years.
RT = n × 100
R × 6 = $3/10$ × 100
R = 5%
As,S.I. = P
S.I. = ${P × R × T}/100$
100 = RT
100 = 5 × T
This is possible only when T = 20.
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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 banks on Rs.500 for 2 years is Rs.2.50. The difference between their (per annum) rate of interest is :
a) 0.25%
b) 0.10%
c) 1.00%
d) 0.50%
Answer »Answer: (a)
${500 × 2 × R_1}/100 - {500 × 2 × R_2}/100$ = 2.5
where $R_1 & R_2$ are rate% of both banks
10 $(R_1 - R_2 )$ = 2.5
$R_1 - R_2 = {2.5}/10$
= 0.25 % per annum
Using Rule 7If the difference between two simple interests is 'x' calculated at different annual rates and times, then principal (P) isP = $ {x × 100}/{(\text"difference in rate") ×(\text"difference in time")}$
Here, P = Rs. 500, x = Rs. 2.50
Difference in time = 2 years.
Difference in rate = ?
500 = ${2.50 × 100}/{(\text"diff.in rate") × 2}$
Different in rate = 0.25%
Question : 2
Simple interest on Rs.500 for 4 years at 6.25% per annum is equal to the simple interest on Rs.400 at 5% per annum for a certain period of time. The period of time is
a) 5 years
b) 4 years
c) 8$2/3$ years
d) 6$1/4$ years
Answer »Answer: (d)
Using Rule 1,
Let the period of time be T years. Then,
${400 × 5 × T}/100 = {500 × 4 × 6.25}/100$
T = ${500 × 4 × 6.25}/{400 × 5}$
= $25/4 = 6{1}/4$ years
Question : 3
Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?
a) Rs.1800
b) Rs.1700
c) Rs.2000
d) Rs.1900
Answer »Answer: (c)
Using Rule 1,
Let the sum lent in each case be x.
Then, ${x × 9 × 2}/100 + {x × 10 × 2}/100$ = 760
${x × 2}/100$(9 + 10) = 760
${2 × 19x}/100$ = 760
$x = {760 × 100}/{2 × 19}$ = Rs.2000
Question : 4
A sum of Rs.1500 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 12.5% per annum for 4 years. The sum lent out at 12.5% is :
a) Rs.1000
b) Rs.500
c) Rs.1250
d) Rs.750
Answer »Answer: (d)
Using Rule 1,
Let the sum lent out at 12.5% be x
Sum lent out at 10% = 1500 - x
Now, ${(1500 - x) × 10 × 5}/100$
= ${x × 12.5 × 4}/100$
50 (1500 - x ) = 50x
2x = 1500
$x = 1500/2$ = Rs.750
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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