[Q] Simple and Compound Interest Tricks - 2

In this post I will give some extremely important formulas that will save your time. Read this post carefully and note down all the formulas in a piece of paper for quick revision.

Q. 1) If a sum of money becomes 3 times itself in 20 years at simple interest. What is the rate of interest?
In such questions apply the direct formula-
Rate of interest = [100*(Multiple factor - 1)]/T
So R = 100*(3 - 1)/20
Answer : 10%
Note : With this formula you can find Rate if Time is given and Time if rate is given.

Q. 2) 

In such questions, just write this line :
1st part : 2nd part : 3rd part = 1/(100+T1 * r) : 1/(100+T2 * r) : 1/(100+T3 * r)
 = 1/(100+2 * 5) : 1/(100+3 * 5) : 1/(100+4*5)
 = 1/110 : 1/115 : 1/120
 = 23*24 : 22*24 : 23*22
Hence 1st part = (23*24)/ (23*24 + 22*24 + 23*22) * 2379
Answer : 828
Note : Surprisingly, such questions when asked mostly have this same data, i.e., R=5% and T1, T2, T3 = 2, 3, 4 years, respectively. Only the Principal is changed. So it would be wise if you can just mug this line :
1st part : 2nd part : 3rd part = 23*24 : 22*24 : 23*22
Based on the above line, you would be able to solve such questions in a jiffy. 
But note that it will only work if the question is on Simple Interest. Like the below question appeared in SSC CGL Tier 2-

Q. 4

Here the data is same. i.e., R=5% and T1, T2, T3 = 2, 3, 4 years, respectively. So we will write directly -
1st part : 2nd part : 3rd part = 23*24 : 22*24 : 23*22
A received = (23*24)/ (23*24 + 22*24 + 23*22) * 7930
Answer : Rs. 2760

Q. 5) If a certain sum of money P lent out for a certain time T amounts to P₁ at R₁% per annum and to P₂ at R₂% per annum, then

The above formula is for calculating the Time, if the question asks the rate, then just interchange the rate and time. Hence the formula will become

R = (P_{1 -} P_2)*100/P₂T_{1 -} P₁T₂

Apply the formula:
R = (650-600)*100/600*6 - 650*4
R = 5%

Alternative Method :

You can solve such questions quickly without mugging the above formula. How?

The sum amounts to Rs. 600 in 4 years and Rs. 650 in 6 years. This means the simple interest is Rs. 50 for 2 years (because the amount increased from Rs. 600 to Rs. 650 in 2 years)

So the SI for 4 years is Rs. 100 (we have seen earlier than SI is proportional. So if SI = 100 for 2 years, then SI = 150 for 3 years, SI = 250 for 5 years and so on)

Now SI = Rs. 100; P = 600-100 = Rs. 500; t = 4 years

R = 100*SI/(P*t) = 10000/2000

Answer: 5%

For CI, the formula is different

Difference between CI and SI

This topic is very important from examination point of view. Note the following things-

If t=1 year, then SI = CI

If t=2 years then difference between CI and SI can be given by two formulas-

 If t=3 years then difference between CI and SI can be given by two formulas-

In all the above formulas we have assumed that the interest is compounded annually

Let us solve some CGL questions

Q. 6

A = P(1+r/100)^t

Given, A=1.44P t = 2 years

1.44P = P(1 + r/100)^2

r = 20%

Answer : (D)

Q. 7

Here the interest is compounded half yearly, so the formulas we mugged earlier are of no use here. We will have to solve this question manually

SI = P*10*1.5/100 = 0.15P

CI = P(1 + 5/100)^3 - P = P(1.05^3 - 1)

Given CI - SI = 244

P(1.05^3 - 1) - 0.15P = 244
P = Rs. 32000

Answer : (C)

Q. 8

Time = 2 years

Hence apply the formula: Difference(D) = R*SI/200

CI - SI = R*SI/200

CI - SI = (12.5/200)*SI

510 = 1.0625*SI    [Since CI = Rs. 510]

SI = Rs. 480

Answer : (D)

       Q. 9

CI for 1st year = 10% of 1800 = Rs. 180

CI for 2nd years = 180 + 10% of 180 = Rs. 198

Total = 180+198 = Rs. 378

Hence time = 2 years

Or you can apply the formula

A = P(1+r/100)^t

Answer : (B)

Q. 10

2.5 = P*R*2/100 - P*r*2/100
2.5 = 10R - 10r
R - r = 0.25
Answer : (D)

       Q. 11

CI for 1st year = 5% of P = 0.05P

CI for 2nd year = 5% of P + 5% of (5% of P) = 0.05P + 0.0025P = 0.0525P

Total CI = 0.05P + 0.0525P = 0.1025P

Given, 0.1025P = 328

P = Rs. 3200

Answer : (C)

Note : You can solve this question by the formula A = P(1+r/100)^t as well

Q. 12

Note that in this question the CI for 2 years in not given, but the CI for the 2nd year is given.

CI for 2nd year = 10% of P + 10% of (10% of P) = 0.1P + 0.01P = 0.11P

Given, 0.11P = 132

P = Rs. 1200

Answer : (D)

Q. 13

Interest = Re. 1 per day = Rs. 365 for 1 year

SI = P*r*t/100

t=1, r=5%, SI = Rs. 365

So, P = 365*100/5 = Rs. 7300

Answer : (A)

Q. 14

We know 

Difference = P(r/100)^2(r/100 + 3)

P = Rs. 10000, r = 5%, t = 3 years

Hence D = Rs. 76.25

Answer : (C)

Q. 15

We know, R = [(y/x)^(1/T2 - T1) - 1]*100

 = [(1587/1200)^1/(3 - 1) - 1]*100

 = [(1587/1200)^1/2 - 1]*100

 = 3/20 * 100

 = 15%

Answer : (B)

So this is the end of CI and SI series. If you have any doubt in this topic, please drop a comment...

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