Aptitude - Simple Interest - Discussion

14. 

A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6% p.a for 2 years. Find his gain in the transaction per year.

[A]. Rs. 112.50
[B]. Rs. 125
[C]. Rs. 225
[D]. Rs. 167.50

Answer: Option A

Explanation:

Gain in 2 years
= Rs. 5000 x 25 x 2 - 5000 x 4 x 2
4 100 100
= Rs. (625 - 400)
= Rs. 225.

Gain in 1 year = Rs. 225 = Rs. 112.50
2

Video Explanation: https://youtu.be/zBjcwqIcmL4


Basudev said: (Jun 11, 2010)  
Where this 25 come from, I don't understand. Please give the proper solution.

Sundar said: (Jun 11, 2010)  
Hi Basudev,

We can write 6(1/4) as 25/4. Both are equivalent to 6.25

I hope you understand what I have mentioned here. Have a nice day!

Bhavya Y J said: (Jun 11, 2010)  
Where we taking this value 25/4 ?

Sheik said: (Jun 25, 2010)  
Its very simple 25/4 is the rate of interests at which he lends it to other person

just find s.i. of 5000,4%,2
and 5000,25/4%,2

and subtract the both pls refer 8th std maths book.

Srinu M said: (Aug 27, 2010)  
The difference between the interests is 2.25.

So interest at 2.25 for 1 year on 5000 is the gain for 1 year

= (2.25/100) x 5000 x 1

= 112.5

Ganesh said: (Jul 30, 2011)  
Every thing here is fine but at last why did you take average of the gain 225/2=125.50.

Please clarify my doubt.

Mandhapalli Suresh said: (Sep 12, 2011)  
Actually you are taking 2 years know that is in which the loan lends to another person but we want actual gain if 2 years is 225 means for 1 year 225/2=112. 5 ok.

Sumit said: (Jan 30, 2012)  
Simplest method to solve
Principle is same
Term i.e period is same
ONLY lending & borrrowing rate differs
So GAIN=Diff between them(25/4-4)% = 9/4%

Therefore gain in rupees = 5000*9/4% = 112.5

Pooja said: (Aug 29, 2012)  
Thanx Sumit..its really simple:)

Mary said: (Feb 11, 2014)  
What is not clear in the qn is whether the interest is lent or the amount is lent after two years?

Bikash said: (Apr 10, 2014)  
CASE 1:
P = 5000, T = 2, R = 4%.

CASE 2:
P=5000, T = 2, R = 6.25%.

GAIN = 6.25% - 4%.
= 2.25%.

NOW, 5000*2.25% = 112.5( FOR 1 YEAR).

Jaya Prakash said: (Jul 6, 2014)  
From where we got 25/4?

Gandham Suresh said: (Nov 27, 2014)  
I really do't know why we have calculated the gain in that way? What is gain? Please send me solution.

Pranav said: (Mar 18, 2015)  
At the place of 25/4, we can write 6.25 which is equal to 25/4. And also we can say (6+1/4) year = 6.25.

Divya S said: (Jun 28, 2015)  
6(1/4).

1 is reminder.
4 is divisor.
6 is quotient.

Finally get the answer 25/4.

Vamsi said: (Jul 16, 2015)  
We can also write 6(1/4) as 4*6+1=25/4.

Rajesh said: (Dec 25, 2015)  
----> 5000*4% = 200.

----> 5000*6.25% = 312.50.

----> 312.50-200 = 112.50.

Answer : 112.50.

Shiva said: (Jun 29, 2016)  
In the question, 6% is given how you have taken 6.25%.

Sakshi said: (Aug 19, 2016)  
What annual investment discharge will discharge a debt of Rs. 1092 due in 3 years at SI 12%?

Please anyone answer this.

Thara said: (Sep 14, 2016)  
Nice explanation. Thank you all.

Kiran said: (Nov 5, 2016)  
Why we taking 25?

Nisha said: (Dec 28, 2016)  
Why have we subtracted to get the gain value?

Sachin said: (Feb 3, 2017)  
Nice solution. Thank you all.

Himanshu Baghel said: (Mar 27, 2017)  
Hi, I have a quesion, please give me the answer.

A man land some part of money 15000rs to A at 10% per annum in S.I. if and something part of B at 7% per annum S.I. such that it receive 3870rs total S.I. after 3 years. Find the sum land to A.

Arun M.K said: (Jun 3, 2017)  
@Himanshu.

x + y = 15000,
0.3x+ 0.21y = 3870,
y = 15000 - x.
Solving we get x = 8000 and y = 7000.
So the sum given to A is 8000.

Sureshkrishna said: (Jun 14, 2017)  
In the given data, everything will be same but rate aloe diff
So (25/4)-4 = 2.25.
Final answer: 5000 * 2.25 = 112.50.

Anirban Amit said: (Jul 10, 2017)  
@Himanshu Baghel

Ans:
For,1st person P=x.
2nd person=15000-x.
So, SI=3870.
(x*10*3)/100+[(15000-x)*7*3]/100=3870.
After calculation answer will be 8000.

Aswin Lal said: (Sep 21, 2017)  
Why was 225 divided by 2 in the last step?

Vallabha Chebiyyam said: (Oct 24, 2017)  
Because 225 is the gain for 2 years(read the Q)
we need to calculate for only 1 year so, 225/2=112.5.

Kareena said: (Nov 28, 2017)  
Why are we dividing 225/2?

Hardik Khirnar said: (Dec 17, 2017)  
How it is possible?

Because here the rate of interest is different for each 2 years. So he gains transaction each year is also different. So the person who is intelligent please clear my concept.

Shahee said: (Mar 26, 2018)  
If the time is different. Then how to calculate the gain?

Ayushi said: (Sep 25, 2018)  
In this question, it is mention that person lends the amount to another person at (6 1/4) 25/4 pa not 25/4pc. then how come we are considering this 25/4 as a percentage?

The answer should be RS. 310.5 according to question. Can anyone clear my this doubt?

Raj said: (Sep 26, 2018)  
How come 2 as the denominator in the last step?

Hussain Ezzy said: (Oct 3, 2018)  
@All.

One can avoid the calculations by simply taking the amount of increase in the rate of interest.

i.e
Gain rate --> 25/4 = 6.25%.
Original Rate --> 4%.
increase = 2.25%.
Therefore, Gain = (5000x2.25)/100 = 112.5 Rs.

Animesh said: (Nov 3, 2018)  
How it is 2/100? Can anyone explain me?

Swar said: (Nov 24, 2018)  
2 denotes the number of years.

i.e T, and R % = 6 1/4 = 25/4 % ie 25/(4x100).

Tejanth said: (May 27, 2019)  
6 (1/4) can written as ((6*4)+1)/4. i.e 25/4.

Niranjan Patil said: (Jul 27, 2019)  
(5000*25)/400 - (5000*4)/100 = 112.50.

Sanjana said: (Aug 18, 2019)  
Why we are taking 25/4 instead of 6/4?

=> 25/4 = 6.25 and 6/4 = 1.5 then, how both are equal?
Why are we adding 6+1/4?

Halappa said: (Aug 31, 2019)  
Please, anyone, explain the formula for me.

Renuka Bhosale said: (Apr 3, 2020)  
How 25/4 is equal to 6/4?

Bipin said: (Apr 13, 2020)  
Hi @Halappa.

The formula of simple interest P*T*R /100.

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