Aptitude - Simple Interest - Discussion

See, it is given that both a&b together combinedly having principal amount of 13,900 for two years having si of 3508.

Now by adding both schemes si's with the total si given for two years by using formula
si = p*t*r/100.

By considering scheme b = 13,900-a,
We can find investment on b scheme.

The formula is (pnr/100).

p=inicial amount,
n=no of years,
r=rate of interest

What is Rs. Stand for?

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.

Is we use the formula ptr/100?

I see. the key issue here is they did not say that they are substituting (total money in - "? scheme-A money in") for "? scheme-B money in".

A part that may be confusing (was for me at first) is the use of x: x being the variable and the multiplicative mechanism. the variable should be noted differently than the multiplication - capitalizing X at least or using * to denote multiplication. Let me draw this out in simple terms.

A = money put into scheme A.
Simple interest for scheme A is 14%

B = money put into scheme B.
Simple interest for scheme B is 11%

3508 is the total interest returned from scheme A and scheme B.

13900 is the total money invested into A and B.
(A + B) = 13900

Because the interest accumulates over 2 years, the interest gained is doubled. Therefore the interests in both schemes are doubled.

(A * 14 * 2)/100 +(B * 11 *2)/100 = total interest gained.

note the 100 in the denominator is because the 14 and 11 are percentages. To simplify things the .14 is represented as 14/100 and .11 to 11/100. The numbers workout in the end without any converting or anything.

since we cannot do anything with the 2 variables A and B, we substitute B for ("total money invested" - A). With this we can solve for just A.

(A * 14 * 2)/100 +((13900- A)* 11 * 2)/100 = 3508

Getting rid of the common denominators yields:

(A * 14 * 2)+((13900- A) * 11 * 2) = 350800

Simplify:
(28 * A)+((13900- A) * 22) = 350800

distribute the 22 into the parenthesis

(28 * A) + (13900 *22) -(22 * A) = 350800
Simplify:
28A - 22A + (305800) = 350800

Add like terms:
6A + (305800) = 350800

6A = 350800 - 305800

A = 7500.

Since A + B = 13900:

7500 + B = 13900

B = 6400

$7500 was initially invested into Scheme A and $6400 was initially invested into Scheme B. At the interest 14% and 10%, Scheme A and Scheme B yielded $3508.

Sorry if it is too simple, i just wanted to make sure there was a little confusion as possible.

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.

Can someone please explain me the 2nd step 28X-22X = 350800 - (13900x22) how it came?

Amount invested is nothing but the principal.

Now principal is divided into two parts.

Therefore P1+P2 = 13900 Rs-------equation no.1.

Now,

S.I with rate 14%=S.I1=(P1*2*14)/100 -----as for two years N=2.

S.I with rate 11%=S.I2=(P2*2*11)/100 -----as for two years N=2.

Therefore total S.I=S.I1+S.I2 ---------equation 2.

But S.I = 3508 Rs.

Therefore Equation 2 becomes,

3508 = [ (P1*2*14)/100 ] + [(P2*2*11)/100 ].

3508 = [ P1*14 +P2*11 ] [2/100]---TAKE 2& 100 common.

(3508*100)/2=[ P1*14 +P2*11 ] -----equation 3.

Solve equation 1 & 3 simultaneously,

Hence P1 = 7500 ----for A scheme at rate 14%.

P2 = 6400 ----for B scheme at rate 11%.

Can anyone tell me how to do this answer easily and fast without using pen ?