"> Word Problem 10 | Job Exam Rare Mathematics (JEMrare)

Word Problem 10

Problem 10: On a certain investment simple interest is applied at certain rate. The amount doubles in 20 years term. After how many years the amount will be quadrupled ?



Solution:

Here are situations of two cases,  First case is given as 20 years period, and second case duration is to be found in which interest amount will be four times !

Case 1

In 20 years period

We know

A=P+I ----------\left ( 1 \right )

Where,

P = Principal amount ( Amount in the beginning or investment amount)

I = Interest on principal amount

A= total amount at the end, which is sum of initial amount and interest incurred.

According to condition, amount ‘A’ doubles in 20 years i-e

A=2P

Put in relation (1), this value of ‘A’, we get

2P = P + I

\Rightarrow I =2 P - P

\Rightarrow I=P -----------(2)

It means interest will be equal to principal amount in 20 years !

Case-2

In second case we want amount ‘A’ to become four times i-e

A=4P

Put this value in eq (1) above, we get;

A=P+I

\Rightarrow 4P=P+I

\Rightarrow 4P-P=I

\Rightarrow I=3P -----------(3)

Now equation (2)  says ‘I’ the interest  will be equal to ‘P’  in 20 years i-e  P is equal to interest of 20 years or we can say ‘P’ is the amount of 20 years. So we can take

P=20 years

So we put P = 20 years in eq(3)

\Rightarrow I=3\times 20

or

I = 60 years

It means after interest of 60 years the amount will be 4 times !

Or we can say in 20 years the amount will be  quadrupled

 

 

 

 

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