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Solved Examples(Set 1) - Simple Interest

1. How much time will it take for an amount of $₹900$ to yield $₹81$ as interest at $4.5\%$ per annum of simple interest?
A. $1$ yearB. $2$ years
C. $3$ yearsD. $4$ years
Discuss
answer with explanation

Answer: Option B

Explanation:

$\text{T}=\dfrac{100×\text{SI}}{\text{PR}} = \dfrac{100 × 81}{900 × 4.5} = 2$
2. Arun took a loan of $₹1400$ with simple interest for as many years as the rate of interest. If he paid $₹686$ as interest at the end of the loan period, what was the rate of interest?
A. $6\%$B. $8\%$
C. $7\%$D. $4\%$
Discuss
answer with explanation

Answer: Option C

Explanation:

Given that T = R

$\text{SI}=\dfrac{\text{PRT}}{100}\\\Rightarrow 686=\dfrac{\text{1400×R×R}}{100}\\\Rightarrow \text{R}^2=49\\\Rightarrow \text{R}=7$

3. A sum of money at simple interest amounts to $₹815$ in $3$ years and to $₹854$ in $4$ years. What is the sum?
A. $₹650$B. $₹700$
C. $₹698$D. $₹690$
Discuss
answer with explanation

Answer: Option C

Explanation:

SI for $1$ year $=854-815=39$

SI for $3$ years $=39×3=117$

Required sum $=815-117=698$

4. A sum fetched a total simple interest of $₹929.20$ at the rate of $8\%$ per annum in $5$ years. What is the sum?
A. $₹2353$B. $₹1223$
C. $₹2563$D. $₹2323$
Discuss
answer with explanation

Answer: Option D

Explanation:

$\text{P}=\dfrac{100×\text{SI}}{\text{RT}}=\dfrac{100×929.20}{8×5}=2323$
5. Mr.Thomas invested an amount of $₹13,900$ divided in two different schemes A and B at the simple interest rate of $14\%$ per annum and $11\%$ per annum respectively. If the total amount of simple interest earned in $2$ years was $₹3508,$ what was the amount invested in Scheme B?
A. $₹6500$B. $₹7500$
C. $₹6400$D. $₹7200$
Discuss
answer with explanation

Answer: Option C

Explanation:

Solution 1

Let investment in scheme A $=x$
Then, investment in scheme B $=(13900-x)$

Total simple interest $=3508$
$\Rightarrow$ simple interest on $x$ for $2$ years at $14\%$ per annum + simple interest on $(13900-x)$ for $2$ years at $11\%$ per annum $=3508$
$\Rightarrow \dfrac{x×14×2}{100}+\dfrac{(13900-x)×11×2}{100}=3508\\\Rightarrow 14x+11(13900-x)=175400\\\Rightarrow (14-11)x+152900=175400\\\Rightarrow 3x+152900=175400\\\Rightarrow x=7500$

Investment in scheme B
$=13900-7500=6400$

Solution 2

$3508$ - interest on $13900$ at $11\%$ for $2$ years = interest on scheme A at $3\%$ for $2$ years
(click here for more clarification on the above statement)

$3508$ has the following two components.
(a) interest on scheme A at $14\%$ for $2$ years
(b) interest on scheme B at $11$ for $2$ years

Interest on $13900$ at $11\%$ for $2$ years can be split into the following two parts.
(a) interest on scheme A at $11\%$ for $2$ years
(b) interest on scheme B at $11\%$ for $2$ years

So, $3508$ - interest on $13900$ at $11\%$ for $2$ years
is equal to
interest on scheme A at $3\%$ for $2$ years

$\Rightarrow$ interest on scheme A at $3\%$ for $2$ years
$=3508-\dfrac{13900×11×2}{100}=450$

$\Rightarrow$ Investment in scheme A
$=\dfrac{100×450}{3×2}=7500$

Investment in scheme B
$=13900-7500=6400$

Comments(17)

profileashwini
2015-03-23 12:45:04 
Simple Interest on certain sum at the rate of 10% per annum for 6 years and 7 years differs by rs.650/- what is the sum ? give me answer fast 
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profileDev
2015-04-05 18:37:09 
Simple interest for one year = 650

PRT/100 = 650
P * 10 * 1/100 = 650
P = 6500
The sum is Rs.6500
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profilenewwave
2014-12-30 09:23:16 
A certain sum of money amounts to Rs.1008 in 2 years and to Rs.1164 in 3.5 years.find the sum and rate of interest.
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profileBratisankar
2015-01-07 20:44:00 
in 3.5 yrs the amount 1164
in 2    yrs the amount 1008 -
___________________________
the 1.5 yrs interest is        156
the 1    yr  interest is   156/1.5  =104
the 2 yrs interest is 208 rs
principal=1008-208=   800
rate of interest=(104/800)*100
                     =13%   
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profileJay
2015-01-04 19:44:29 
Let the amount be P and rate of interest be R%

Simple Interest on P for 2 years = (1008-P)
P * 2 * R/100 = (1008-P)
2PR = 100(1008-P) ----(eq:1)
 

Simple Interest on P for 3.5 years = (1164-P)
P * 3.5 * R/100 = (1008-P)
3.5PR = 100(1164-P) ----(eq:2)


(eq:1)/(eq:2) 2/3.5 = 100(1008-P)/100(1164-P)
20/35 = (1008-P)/(1164-P)
4/7 = (1008-P)/(1164-P)

4(1164-P) = 7(1008-P)
4656 - 4P = 7056 - 7P
3P = 2400
P = 800

From eq1, 2*800*R = 100(1008-800)
2*800*R = 100*208
R = 13
Rate of Interest is 13%
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profileSuhani
2014-09-24 06:42:15 
A alone can complete a work in 16 days and B alone in 12 days. Starting with A,they work on alternate days. The total work will be completed in how many days? please tell answer.
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profileRajeev
2016-09-10 09:50:26 
A-16                - 3
B-12   LCM:48   - 4

A+B 2 days - 7

48/7 = 6
balance: 48-42 = 6
A- 3 (13th day)
B- 3, (3/4 day)

Ans: 13 3/4 days.
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profileDev
2014-09-30 21:32:13 
Work done by A in 1 day is 1/16 and work done by B in 1 day is 1/12

In day 1, only A works and total work gets completed = 1/16
In day 2, only B works and total work gets completed = 1/12
this pattern continues till total work gets completed

Work completed in every 2 days = 1/16 + 1/12 = 7/48
So in 2*6 = 12 days,  6*7/48 = 42/48 = 7/8 work gets completed

in 13th day, total work gets completed = 7/8 + 1/16 = 15/16

Remaining work = 1/16
days taken by B to complete this = (1/16)/(1/12) = 3/4 days

So total work gets completed in 13 3/4 days
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profileAthira
2015-01-07 19:34:21 
3w/d--->A---16             (1)

4w/d---->B---12            (2)
.........................
7w/d---->A+B....48w

TOTAL DAYS =13 3/4 days

A

3W

B

4W

A

3W

B

4W

A

3W

B

4W

A

3W

B

4W

A

3W

B

4W

A

3W

B

4W

A

3W

B

3W

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profileAkshay
2015-09-09 11:25:21 
Athira, Couldn't able to understand the equations you made.
Pls explain
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