# Aptitude - Simple Interest - Discussion

Discussion Forum : Simple Interest - Data Sufficiency 2 (Q.No. 1)
Directions to Solve

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1.
 What is the principal sum? I. The sum amounts to Rs. 690 in 3 years at S.I. II. The sum amounts to Rs. 750 in 5 years at S.I. III. The rate of interest is 5% p.a.
I and III only
II and III only
I and II only
I and III only, or II and III only
Any two of the three
Explanation:

Clearly, any two of the three will give us the answer.

Discussion:
31 comments Page 1 of 4.

HRK said:   2 years ago
Using I and III;
Let S.I be 'x'.
Hence, P = 690 - x.
x = [(690- x) *5*3] / 100.
Solve for 'x' and find P.
Similarly, it works using II and III

Now, using I and II.
Let x be the interest rate.
Hence, P + 3Px = 690, simplify to P(1+3x) =690 -----> (a)
P + 5Px = 750, simplify to P(1+5x)=750 -----> (b).

Now dividing a by b, P gets canceled and solves for x.
x = 0.05 or 5%.
Now substitute x in the equation a or b to get P.

So we can use any of the three to solve.
Thanks.
(3)

Karuppaiya said:   3 years ago
As Simple as Like that, I will explain here;

Given as Statement 1: P = 690 N= 3 yrs.
Given as Statement 2: P = 750 N= 5 yrs.
By Using these statements We get SI for 2 yrs is (750-690 = 60).

Therefore; SI for 1 yr is 30.

So, SI for 3 yrs will be 90 and that of for 5 yrs will be 150.
We know that Amount = Principal + SI.
Here for 3 yrs W.K.T SI is 90 and Amount is 690.
and therefore Principal is 690-90=600.
And by using statements 2 and 3 we can solve by the following method.
P + (P*5*5)\100 = 750.
100P + 25P = 750*100.
125P = 75000.
P = 600.
(2)

Manthan said:   3 years ago
As Amount = principal+ SI.

Where si= prt/100.
This is the basic formulae that are applied here.

If suppose we take equationn 1 and 2 then,
P + P.3.r% = 690---(1)
P + P.5.r% = 750---(2)

Divide equation 1 by 2 to get r and then p,

And if we take eqn 1 and eqn 3 we will get;
"P=(100*si)/(r*t) ".

Vidya sree said:   3 years ago
Thank you @Ashish.

Effoti said:   6 years ago
By using I and II;

S.I for 2 years = 750-690 = 60 as S.I is divided uniformly for each year, For 1 year = Rs. 30 and For 3 year = 90,
Principal = 690-90 = 600.

By using II and III
As Total Sum = Principal + Interest i.e 750 = P + I (after 5 years) ------> (1)
P = I *100 / R * T = I *100 / 5*5 = 4I,
Put value of P in eq. 1, 750 = 5I , I = 150 and P = 750 -150 = Rs. 600,

Similarly By using I and III.
P = I *100 / R*T = I*100/5*3 = 20/3(I),
690 = 20/3(I) + I , By solving this we get I = Rs.90 and P = 690 - 90 = Rs. 600.

Hence answer is E Any two of the three.

Mansi Arora said:   6 years ago
Hi @Aryan,

We are using here all the three given statements to get the value of P which is not given in the options.

P V Snehil said:   6 years ago
We cannot get P using I and II, as we donot know the are when we have only these two statements.

(1)

Shruthi said:   6 years ago
If it is any two of the 3 then there is a possibility of taking 1 and 2.

How can we get p using 1 and 2?

Girish said:   7 years ago
690 - P = 3PR.
750 - p = 5PR.

Dividing both equations
(690 - P)/(750 - P) = 3/5.
-> (690 - P)5 = (750 - P)3.

By solving;

P = 600.
(1)

T.Prabhu Pandiyan. said:   8 years ago