Aptitude - Simple Interest - Discussion
Discussion Forum : Simple Interest - General Questions (Q.No. 2)
2.
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
Answer: Option
Explanation:
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).
| Then, |  |
x x 14 x 2 |  |
+ | |
(13900 - x) x 11 x 2 | |
= 3508 |
| 100 | 100 |
28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.
Video Explanation: https://youtu.be/Xi4kU9y6ppk
Discussion:
115 comments Page 2 of 12.
PRANAV said:
9 years ago
@Bushra.
Area of rectangle = l * w
Perimeter of rectangle = 2 * (l + w)
--------------------------------------------
2 * (l + w) = 200
l + w = 100 ---> equa(1)
l * w = 2400
so, w = 2400/l ---> equa(2)
Putting equa(2) in equa(1).
We get,
l + (2400/l) = 100
l^2 + 2400 = 100 * l
l^2 - 100 * l -2400 = 0
l^2 - 60 * l - 40 * l -2400 = 0
l (l - 60) - 40 (l - 60) = 0
(l - 60) (l - 40) = 0
Hence, if l = 60 w = 40 (from equa(1))
Else, l = 40 then w = 60.
Area of rectangle = l * w
Perimeter of rectangle = 2 * (l + w)
--------------------------------------------
2 * (l + w) = 200
l + w = 100 ---> equa(1)
l * w = 2400
so, w = 2400/l ---> equa(2)
Putting equa(2) in equa(1).
We get,
l + (2400/l) = 100
l^2 + 2400 = 100 * l
l^2 - 100 * l -2400 = 0
l^2 - 60 * l - 40 * l -2400 = 0
l (l - 60) - 40 (l - 60) = 0
(l - 60) (l - 40) = 0
Hence, if l = 60 w = 40 (from equa(1))
Else, l = 40 then w = 60.
Manish Kumar said:
7 years ago
In this question money is divided into two parts. On one part he got 14% interest and on other part he got 11%.
The difference is 3%(14%-11%) in one year.
If we got 14% on both then 14% of 13900 = 1946.
But we got interest 3504 which is in two years so in one year 3504/2 =1754.
The difference is 1946-1754=192.
So we got 3% difference on 192.
3% =192.
1%=192/3=64.
100%=6400.
So, one part is 6400 and other (13900-6400) = 7500.
The difference is 3%(14%-11%) in one year.
If we got 14% on both then 14% of 13900 = 1946.
But we got interest 3504 which is in two years so in one year 3504/2 =1754.
The difference is 1946-1754=192.
So we got 3% difference on 192.
3% =192.
1%=192/3=64.
100%=6400.
So, one part is 6400 and other (13900-6400) = 7500.
Ashok said:
9 years ago
It can simply solve like this using allegation concept as;
Total amount can be given in 2 types of interests as one A is @14% & B is @11%.
He gets average in totally 2 years is given 3508/2 = 1754.
Its mean % is 1754/13900 = 12.6%.
Apply Allegation principle on interests.
Then, we get;
-> A : B.
-> 8 : 7.
Totally we have 15 parts = 13900
We require the amount invested in Scheme:
B = 7/15 * 13900.
=> 6486 (approx).
Total amount can be given in 2 types of interests as one A is @14% & B is @11%.
He gets average in totally 2 years is given 3508/2 = 1754.
Its mean % is 1754/13900 = 12.6%.
Apply Allegation principle on interests.
Then, we get;
-> A : B.
-> 8 : 7.
Totally we have 15 parts = 13900
We require the amount invested in Scheme:
B = 7/15 * 13900.
=> 6486 (approx).
Bikash kumar said:
1 decade ago
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).
Then, (X*14*2/100)+{(13900-X)*11*2/100} = 3508.
28x/100 + (13900*22)-(x*22)/100 = 3508.
28x/100 + 305800-22x/100 = 3508.
28x+305800-22x/100 = 3508.
Now,
28x+305800-22x=3508*100.
28x-22x=350800-305800.
6x=45000.
x=45000/6.
x=7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.
Then, (X*14*2/100)+{(13900-X)*11*2/100} = 3508.
28x/100 + (13900*22)-(x*22)/100 = 3508.
28x/100 + 305800-22x/100 = 3508.
28x+305800-22x/100 = 3508.
Now,
28x+305800-22x=3508*100.
28x-22x=350800-305800.
6x=45000.
x=45000/6.
x=7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.
Vinoth kumar said:
1 decade ago
Here 3508 is a total interest.
Say 3500. 3500 is approximately 25% of 14000 (13900). So for one year it slightly more than 12.5%. So invest in A (14%) must be more.
So the answer must be less than 6950(13900/2). Two opinion A are B. Now pair up. (6400/7500) or (6500/7400).
Take any one pair find out their simple interest. And then add up both SI which result in 3508 is the answer.
Say 3500. 3500 is approximately 25% of 14000 (13900). So for one year it slightly more than 12.5%. So invest in A (14%) must be more.
So the answer must be less than 6950(13900/2). Two opinion A are B. Now pair up. (6400/7500) or (6500/7400).
Take any one pair find out their simple interest. And then add up both SI which result in 3508 is the answer.
Jitender said:
8 years ago
Simple interest for two year 3508, therefore simple interest for one year will be1754
x+y=13900 ---> Equation (1).
14x+11y=175400 ---> equation 2.
To solve the equation we are multiplying the equation 1 by 14.
14x+14y=194600 ---> equation 1 after multiply by 14.
14x+11y=175400.
After subtracting the equation we will get.
3y = 19200,
Y = 6400.
x+y=13900 ---> Equation (1).
14x+11y=175400 ---> equation 2.
To solve the equation we are multiplying the equation 1 by 14.
14x+14y=194600 ---> equation 1 after multiply by 14.
14x+11y=175400.
After subtracting the equation we will get.
3y = 19200,
Y = 6400.
Subham Prakash said:
3 years ago
@Priya @Swathi @Kasamsetty Deepshika.
A:14% for 2 years = 28% (In si rate of interest is same for every year i.e. for 2yrs 14 is directly multiplied).
B:11%for 2years = 22%.
28% of principal13900=3892 (interest) but the interest of A+B scheme is given=3508.
i.e 384 extra (3892-3508) =384.
28%~22%=6%.
6%---> 384.
100%---> 6400.
A:14% for 2 years = 28% (In si rate of interest is same for every year i.e. for 2yrs 14 is directly multiplied).
B:11%for 2years = 22%.
28% of principal13900=3892 (interest) but the interest of A+B scheme is given=3508.
i.e 384 extra (3892-3508) =384.
28%~22%=6%.
6%---> 384.
100%---> 6400.
(211)
Yogeswara Rao said:
5 years ago
Invested money = 13900.
Divided into two schemes A and B.
Let the scheme A = x.
Scheme B = 13900-x.
SI = PTR/100.
SI = x.2.14/100,
SI = 28x/100.
2nd case
SI = (13900-x).2.11/100.
SI = 3508,
3508 = 28x/100+ (13900-x).2.11/100,
350800= 28x +305800-22x,
-45000 = -6x.
X = 45000/6.
X = 7500.
B = 13900 - 7500.
B = 6400.
Divided into two schemes A and B.
Let the scheme A = x.
Scheme B = 13900-x.
SI = PTR/100.
SI = x.2.14/100,
SI = 28x/100.
2nd case
SI = (13900-x).2.11/100.
SI = 3508,
3508 = 28x/100+ (13900-x).2.11/100,
350800= 28x +305800-22x,
-45000 = -6x.
X = 45000/6.
X = 7500.
B = 13900 - 7500.
B = 6400.
(12)
Tushar waghchaure said:
8 years ago
Let's assume any answer between option, suppose 6400,
and total amount is given 13900 so, 13900-6400=7500 so we got two values of principle(p),
we know formula i,e SI= P*R*T/100.
so put value...SI=7500*14*2/100=2100 AND SI=6400*11*2/100=1408 and addition of this is =3508. So, A invest 7500 AND B invest 6400.
and total amount is given 13900 so, 13900-6400=7500 so we got two values of principle(p),
we know formula i,e SI= P*R*T/100.
so put value...SI=7500*14*2/100=2100 AND SI=6400*11*2/100=1408 and addition of this is =3508. So, A invest 7500 AND B invest 6400.
Rajesh said:
1 decade ago
Assume the amount invested in scheme B be 6400.
Then the amount invested in scheme A is 13900-6400 = 7500.
14% in 7500 = 1050.
For two years (1050*2) = 2100.
11% in 6400 = 704.
For two years (704*2) = 1408.
Adding these two gives (2100 + 1408) = 3508.
Therefore we assumed correctly and the answer is 6400.
Then the amount invested in scheme A is 13900-6400 = 7500.
14% in 7500 = 1050.
For two years (1050*2) = 2100.
11% in 6400 = 704.
For two years (704*2) = 1408.
Adding these two gives (2100 + 1408) = 3508.
Therefore we assumed correctly and the answer is 6400.
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