type 4 difference & equality of si rate & years Practice Questions Answers Test with Solutions & More Shortcuts
simple interest PRACTICE TEST [6 - EXERCISES]
type 1 basic simple interest using formula
type 2 increase or decrease in interest rate
type 3 money multiples in ‘n’ years
type 4 difference & equality of si rate & years
type 5 si on ‘n’ years & ‘x/y ‘of sum
type 6 si with ratios
Question : 16 [SSC CPO S.I.2009]
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 : 17 [SSC CGL Prelim 2002]
A sum of Rs.1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. The interest on each part (In rupees) is
a) 65
b) 60
c) 40
d) 70
Answer »Answer: (b)
Using Rule 1,
Let first part be x and second part be(1750 –x )
According to the question,
x × $8/100 = (1750 - x ) × 6/100$
8x + 6x = 1750 × 6
14x = 1750 × 6
$x = {1750 × 6}/14$ = Rs.750
Interest = 8% of 750
= 750 × $8/100 = Rs.60
Question : 18 [SSC CPO S.I.2009]
Equal sum of money are lent to X and Y at 7.5% per annum for a period of 4 years and 5 years respectively. If the difference in interest, paid by them was Rs.150, the sum lent to each was
a) Rs.1000
b) Rs.500
c) Rs.3000
d) Rs.2000
Answer »Answer: (d)
Let the sum lent be x.
${x × 7.5 × 5}/100 - {x × 7.5 × 4}/100 = 150$
${x × 7.5 × 1}/100$ = 150
$x = {150 × 100}/{7.5}$ = Rs.2000
Using Rule 13,
Here, $P_1 = P, R_1 = 7.5%, T_1$ = 4 years.
$P_2 = P, R_2 = 7.5%, T_2$ = 5 years.
S.I. = Rs.150
S.I. = ${P_2R_2T_2 - P_1R_1T_1}/100$
150 = ${P × 7.5 × 5 - P × 7.5 × 4}/100$
15000 = 7.5P
P = $15000/{7.5}$
P = $150000/75$ = Rs.2000
Question : 19 [SSC CHSL 2010]
In how many years will the simple interest on a sum of money be equal to the principal at the rate of 16$2/3$% per annum ?
a) 5 years
b) 4 years
c) 8 years
d) 6 years
Answer »Answer: (d)
Using Rule 1,
Let the principal be x.
Time = $\text"SI × 100"/\text"Principal × Rate"$
= ${x × 100 × 3}/{x × 50}$ = 6 years
Question : 20 [SSC CHSL 2015]
The difference between simple interest and the true discount on Rs. 2400 due 4 years hence at 5% per annum simple interest is
a) Rs.70
b) Rs.30
c) Rs.50
d) Rs.80
Answer »Answer: (d)
Using Rule 1,
True discount
= $\text"Amount × Rate × Time"/ \text"100 +(Rate × Time)"$
= ${2400 × 5 × 4}/{100 + (5 × 4)}$
= ${2400 × 5 × 4}/120$ = Rs.400
S.I. = ${2400 × 5 × 4}/100$ = Rs.480
Required difference
= Rs.(480 - 400) = Rs.80
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type 4 difference & equality of si rate & years Shortcuts »
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Click to Start..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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