Aptitude - Simple Interest - Discussion

C let us assume that principle invested in a is x.

& b be y.

The total amt invested is 13900,
so x+y=13900 or y=13900-x,
by using formula i=ptr/100,
x*14*2/100 + y*11*2/100,
= 28x/100+22y/100=3508,
28x+22y=350800,

Substitution of y frm 1
28x+22(13900-x) = 350800 now solve.

Why it has not taken X for B's principal? Please explai me.

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.

Let calculate SI for 14% per anum si = 13900*1*14/100 = 1946,
Caluculate si for 11% per anum si = 13900 * 1 * 11/100 = 1529,

Given intrerest for 2 year so 3508/2 = 1754 p.a.
By using alligation:

1956-1754 = 192
1754 - 1529 = 225.

Tatio;-B:A = 192 : 225.

Sum of B = 13900 * 192/417 = 6400.

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%.

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.

@Renu.

It has Some correction @Phani Kumar .

Given -----> P = P1+P2 (Principle is divided between two)
Sum of interests on P1 and P2 is given as I = SI1+ SI2 = 3508 S11---> Simple interest on P1
SI2 ---> Simple interest on P2
I = ( P1*T1*R1 /100) + (P2*T2*R2/100)
100*I = (P1*T1*R1) + (P2*T2*R2)
But Given T1= T2=T
so,
100*I /T = P1*R1 + P2*R2
= P1*R1 + (P-P1)*R2
= P1*R1 + P*R2 - P1*R2

(100*I/T) - P*R2 = P1*(R1-R2)
((100*I)-( P*T*R2))/ T = P1*(R1-R2)
P1 = (100*I - P*T*R2) / T*(R1-R2) (R1-R2 = 14 -11 =3)
Find P2 = P - P1

Good explanation. Thank you all.

Thank you so much @Jitendar.

P=13900
A=14%
B=11%
So,total SI= 3508.

Hence we need to fine out B scheme.
Use option given 1st option is 6400,
6400*2 year*11%÷100=1408,
And remaining intrest is 3508-1408=2100,
Now A scheme,
13900-6400=7500,
7500*2year*14%÷100=2100.