Aptitude - Simple Interest - Discussion

1. 

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

[A]. Rs. 650
[B]. Rs. 690
[C]. Rs. 698
[D]. Rs. 700

Answer: Option C

Explanation:

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.


V.Malarvizhi said: (Jul 20, 2010)  
Why not applied principal formula si*100/r*t ?

Jayesh said: (Aug 21, 2010)  
Can the formula be SI*100/R*T ?

Name said: (Sep 6, 2010)  
3y--815,
4y--854,
----------
1y--39,

So, 3y ---39 x 3 = 117

Principal is = (815-117) = 698

Kannan said: (Nov 25, 2010)  
Why should not subsract with 854? Please clear my doubt....

Priya said: (Nov 29, 2010)  
@Lavanya and kanna

To get 1 year difference we have to subtract
4year amount-3year amount
this difference amount is the 1 year simple interest..
that's why..
Rs. (854 - 815) = Rs. 39
39 is 1year S.I.

hope it helps you..

Nag said: (Feb 8, 2011)  
Thank you. This is explanation is very helpful for me.

Appu said: (Feb 21, 2011)  
Hai friends,

Principle is the amount borrowed. Here, explain about SI of 3 years and 4 years. Assume P is the principal then, P+854 for 4 years and p+815 for 3yrs.

So here it is necessary to find the SI of one year and subtract it from the 3 year or 4 year.

That is, (815-117) = 698 and 854-156=698.

Vishnu said: (Mar 8, 2011)  
To get a si of one year or it might be two years if it is two year we have to divide it by two si=3yrs -2yrs willl give u one year si why should we have to go to risk.

Ramesh said: (Mar 18, 2011)  
PTR/100 = 815
P*3*R/100 = 815
R/100=854- 815
p * 3 * 39 = 815
P * 117 = 815
p = 815-117 = 698

Hari said: (Mar 26, 2011)  
I like this type of solutions thank you

I think this answer also

1year 854-815=39

3years 39*4=156

854-156=698

Vijay said: (May 27, 2011)  
What is formula of simpe interest ?

Rajini Kumar said: (Jun 3, 2011)  
S.Ib = PNR/100

Narasimha Reddy said: (Jun 4, 2011)  
S.I=PTR/100

Gayathri said: (Jun 22, 2011)  
Hi Friends!
Principle = the amt u borrowed
Interest = the small additional amt u pay for the amt u
borrowed

First let me explain u d question
In the question,
A sum of money at simple interest amounts to Rs. 815 in 3 years means the Principle amt together wit the interest paid for 3 yrs is Rs. 815 and similarly Principle amt together wit the interest paid for 4 yrs is Rs. 854

Therefore, if we subtract (854-815) we get the simple interest for 1 year as Rs. 39

Then, we calculate simple interest for 3 yrs as (39*3)= 117

Next step, we subtract (815 - 117) to get Principle amt for a yr as Rs. 698

Brief explanation for last step:

815 = Principle amt + int for 3 yrs ......equation 1
117 = int for 3 yrs ......equation 2

now subtract both equations, we get the principle amt

I hope tat this explanation will be helpful to u

Reshmi said: (Jul 6, 2011)  
Thank you gayathri. You explained well.

Prathap said: (Jul 6, 2011)  
Simple and clear explanation by gayatri.

Raghu Karthic said: (Jul 28, 2011)  
Superb explanation gayathri. Thanks a lot.

Ashik said: (Jul 30, 2011)  
S.I for one yr=854-815=39
for 4 years=4*39=156
hence,854-156=698

i think it will be simple....

Vikram said: (Aug 2, 2011)  
According to the question,

SI + P = 815 in three years and
SI + P = 854 in four years

so 815 - P = SI and
854 - P = SI
Therefore,

815 - P = (P * 3 * R)/100 and ---- eq 1
854 - P = (P * 4 * R)/100 ---- eq 2
Now,
eq 1 / eq 2 gives

(815 - P)/(854 - P) = 3/4
Solving this eq, we get
P = 698

Uma said: (Aug 16, 2011)  
@gayathri your explination is very helpfull.

Thank you.

Harsh said: (Sep 13, 2011)  
I am not deciding which is easiest way to solve of the given question so please suggest me.

Venkatesh said: (Sep 19, 2011)  
Gayathri thank you so much before that I want to say myself I am dull even though I understood you are explantion it is very clear keep it up.

Jaya said: (Sep 26, 2011)  
Gayathri thanks a lot its vry clr & simple

Kichu said: (Oct 24, 2011)  
Thanks gayathri.

Muskan said: (Nov 20, 2011)  
Please give me the solution of this question.

A certain sum given on simple interest became double in 20 years. In how many years will it be 4 times.

Ranjitha said: (Dec 27, 2011)  
Its same friends.. you can do it in either way
(39*4)=156
854-159=698 only

Sonia said: (Dec 29, 2011)  
Thanks Gayathri. Really your explanation is helpful.

Venkatesh Kumar said: (Jan 17, 2012)  
Thanks Gayathti for giving detailed explanation.

Saurabh said: (May 1, 2012)  
Thanks gayathri.

Tejashree said: (Jun 8, 2012)  
Thanks gayathri

Radhika said: (Jun 23, 2012)  
Thank you so much Gayathri.... very good explaination

Moksh said: (Jul 21, 2012)  
@Gayathri.

Thanks a lot dear.

Very useful answer :).

Ismail Khan said: (Aug 17, 2012)  
Amount for three years is 815
so AMOUNT= p + SI
A = p + pin
815= p + 3pi.......... (1)
similerly for 4 years
854 = p +4pi..........(2)
subtracting equation (1) from(2) we get
39 = pi
or
pi =39
put this value of pi in equation (1) we get
815= p+ 3*39
815= p+ 117
815-117=p
p=698

Satish said: (Sep 3, 2012)  
@Gayahthri explained good .

Sudesna said: (Sep 4, 2013)  
When we apply the formula SI = PRT/100.

And when we apply the formula Amount = P+SI.

Sumit Singh said: (Dec 23, 2013)  
815 ------ 854 (This value 39 increase in 1 year ).

So in four year 39*4/156.

This 156 is interest in four year.

So principle is equal to / 854-156 equal to 698.

Varunraj said: (Jan 4, 2014)  
If we take for four years.

39*4 = 156.

854-156 = 698 is the answer.

If we take three years.

39*3 = 117.

815-117 = 698 the answer is same !

We can do both the way.

Ravi said: (Mar 28, 2014)  
If in this question asked rate also then how to solve this question?

Nishan said: (Jul 10, 2014)  
In my view the interest between the 3rd & 4th year of Rs. 39/- cannot determine the same interest component for the first three years as the interest will be paid on top of the capital?

As such the interest component should reduce proportionately over the previous years?

Narendra said: (Aug 13, 2014)  
SI1 = 815.
SI2 = 854.

DIFFERENCE = SI2-SI1.
D = 854-815.
D = 39.

FOR 3 YEARS = 3*39.
= 117.

SO NOW P = 815-117.
P = 698.

Rafee And Guru said: (Aug 19, 2014)  
Hi Friends!

Principal = the amount you borrowed.
Interest = the small additional amount you pay for the amount you borrowed.

First let me explain you the question.
In the question,

A sum of money at simple interest amounts to Rs. 815 in 3 years means the Principal amount together with the interest paid for 3 yrs is Rs. 815 and similarly Principal amount together with the interest paid for 4 yrs is Rs. 854

Therefore, if we subtract (854-815) we get the simple interest for 1 year as Rs. 39.

Then, we calculate simple interest for 3 yrs as (39*3) = 117.

Next step, we subtract (815 - 117) to get Principal amt for a yr as Rs. 698.

Brief explanation for last step:

815 = Principal amt + int for 3 yrs ......equation 1.
117 = int for 3 yrs ......equation 2.

Now subtract both equations, we get the principal amount

I hope that this explanation will be helpful to you.

Priyanka said: (Nov 16, 2014)  
Hi friends.

Here goes the explanation,

SI for 4 years = Rs 854.
SI for 3 years = Rs 815.

{4-3} = 1.

So SI for 1 year can be {854-815}.
= Rs 39.

So the SI for 3 years can be {39*3}.
= 117.

So principal is 815-117.
= RS 698{ANS}.

Magesh said: (Nov 23, 2014)  
For four years the interest is,

854-815 = 39.
39*4 = 156.

So 854-156 = 698.

It may simple one no need to apply any formulas here. Time waste one.

Stuti said: (Mar 21, 2015)  
Hi.

There is a simple shortcut for solving this question.

P/Sum = A1n2-A2n1/n2-n1.

= 815*4-854*3/4-3.

= 3260-2562/1 = 698.

Shaminzu said: (Jul 20, 2015)  
3y---815.
4y---854.
------------
1y---39.

3y---39*3 = 117 or 4y---39*4 = 156.

815-117 = 698 or 854-156 = 698.

So we could subtract by 854 or 815.

All The best. Think smart.

Monika said: (Oct 16, 2015)  
Can explain me logic behind it?

Prasad said: (Oct 29, 2015)  
Will you elaborate it in understanding way?

Md Sahil said: (Jan 9, 2016)  
Sum amounts to 815 in 3 years.

Sum amounts to 854 in 4 years.

Find sum?

Let the sum be Rs. x.

x = principal amounts in 3 years = Rs. 815.

x = principal amounts in 4 years = Rs. 854.

Principal amount in 1 year = 39 I.

Interest of 1 year = Rs. 39.

Interest of 3 year = 3x39= Rs. 117.

Principal = x.
Rate = ?
Time = 3 years.
For 3 years.

Interest = Rs. 117.
Amount = Rs. 815.
Time = 3 years.

Let rate = R%.
A = p+I.
P = A-I.

= R(815-117).

Rate 698 answer.

Naren said: (Feb 9, 2016)  
815-p = 3*x.1 -----> equation 1.

854-p = 4*x.2 -----> equation 2.

Divide equation 1 with equation 2.

Sumair Mudliar said: (Jun 3, 2016)  
@Md Sahil.

Thank you for explaining the solution.

Imran Syed said: (Jun 18, 2016)  
For simple interest, this formula is very helpful.

That is I = Prt.

Salomi said: (Jun 27, 2016)  
@Gayathri.

Thank you for explaining the solution clearly.

Kabali said: (Jul 6, 2016)  
@Gayathri nice explanation.

Mick Sudama said: (Jul 10, 2016)  
Here you can do it by another S. I 1 yr = 39, in 4 years =156, & principle=854 - 156 = 698.

Aparna said: (Jul 22, 2016)  
Crystal clear explanation, Thanks @Gayathri.

Kitty said: (Jul 24, 2016)  
@Appu.

Your explanation is good, Thank you.

Sachin said: (Jul 27, 2016)  
Thanks @Vikram and @Gayatri.

Sahid Hussain said: (Aug 5, 2016)  
Let the sum is Rs. X and rate of interest is y%.

We know A = P + SI where SI = (P * R * T) /100 Therefore, A = P + (P * R * T) /100.

Case 1 : A = 815, P = x, T = 3 years, R = y%.
A = x + (x * y * 3) /100->1

Case 2 : A = 854, P = x, T = 4 years, R = y%.

A = x + (x * y * 4) /100 ->2

Subtracting equation (1) from equation (2), we get x * y = 3900.

Now by putting this value of x * y = 3900 in any one of above two equation, we'll get sum = x = 698 Answer.

Rakesh.H said: (Aug 11, 2016)  
I will explain in a simple way.

We have A = P + I.

815 = P + I -----> Eq 1.

854 = P + I -----> Eq 2.

Subtract Eq 1 and 2.

Simple interest I = 815 - P - 854 + P

= 39 for 1year.

Then take for 3 years or 4 years.

You will get the same answer.

For 3 years:

39 * 3 = 117.

Or For 4 years:

39 * 4 = 156.

Then use formula A = P + I.

For 3 years:

815 = P + 117,

P = 815 - 117,

= 698.

For 4 years:

854 = P + 156,

P = 854 - 155,

= 698.

Take for 3 or 4 years answer will be same. I think the explanation is very useful.

Aryan said: (Aug 15, 2016)  
Let principal = x,

Principal + simple interest = total sum (after any number of years),

For 3 years,

X + x * r * 3 = 815 ----> Eqution 1,

For 4 years,

X + x * r * 4 = 854 ----> Equation 2,

Now there are 2 unknown and 2 equations solve for x and we get.

X = 698.

Rahul Dev Singh said: (Sep 20, 2016)  
If certain principal amounts to A1 in T1 year and to A2 in T2 year ,then the sum is given by = A2 .T1--A1.T2
_____________
T2--T1
Now use the formula
= 854 * 3 -- 815 * 4
________________
4--3
= 2562--3260
____________
1
= 698.

Karthikeyan said: (Oct 3, 2016)  
@Gayathri.

Superb explanation, You are genius Thank you.

Chirag said: (Oct 19, 2016)  
@Rahul.

How? Please explain your solution clearly.

Tanuja said: (Oct 22, 2016)  
Yeah, this is the very easy solution. But can you explain this method with some other examples?

Like 9 years SI is 657 and 5 years SI is 555 so then?

Ryan said: (Nov 17, 2016)  
@Tanuja

Use Vikram's explanation as reference

In case you didn't understand still, just logically understand that the:

Resultant sum = Principal + (SI * No. of years).

In the case of your example which is 9 years SI is 657 and 5 years SI is 555 so:

P + 9SI = 657 -------------(1)
P + 5SI = 555 -------------(2)

Subtracting (1) with (2) you get:

4SI= 102,
SI = 102/4,
=> SI = 25.5.

Substituting SI in (1) equation you get:

P + 9 (25.5) = 657,
P = 657 - 9 (25.5),
=> P = 427.5.

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