A sum of money triples itself in 3 years at a simple interest. In how many years will it multiply five times?

a)
5 years

b)
8 years

c)
4 years

d)
6 years

e)
None of these

Correct answer is option 'D'. Can you explain this answer?

Question

A sum of money triples itself in 3 years at a simple interest. In how many years will it multiply five times?

a)
5 years
b)
8 years
c)
4 years
d)
6 years
e)
None of these

Correct answer is option 'D'. Can you explain this answer?

Answer

The correct option is Option B.

For 3 yrs

SI = P*R*T/100

3P-P = P*R*3/100

2P = 3P*R/100

R = 200/3

Money will become 5 times

5P - P = (P*200/3*T)/100

4P = (2/3P)T

T = 6

Money will become five times in 6 years

Answer

First of all , the answer given here is incorrect .

The correct answer is 6 years .

SHORTCUT METHOD :-

(TIMES - 1) / YEAR = (TIMES - 1) / YEAR ;

TIMES - represent's doubles itself,triples itself etc...,

Now ,
( 3-1)/3 =( 5-1)/n ;

2/3 = 4/n ;

n = 6 years ;

Answer

Solution:

Let's assume the initial sum of money is 'P'.

Given that the sum of money triples itself in 3 years at a simple interest, we can calculate the simple interest earned in 3 years.

Using the formula for simple interest, we have:

Simple Interest (SI) = (P * R * T) / 100

Where:
P = Principal amount (initial sum of money)
R = Rate of interest per annum
T = Time period in years

Since the sum of money triples itself in 3 years, the final amount after 3 years will be 3P.

Therefore, the simple interest earned in 3 years is:

SI = 3P - P = 2P

To find the rate of interest, we divide the simple interest by the product of the principal amount and the time period:

R = (SI * 100) / (P * T)

Substituting the values, we get:

R = (2P * 100) / (P * 3)
R = 200 / 3

Now, we need to find the time period in which the sum of money will multiply five times.

Let's assume the required time period is 't' years.

Using the formula for compound interest, we have:

Final Amount (A) = P * (1 + R/100)^t

Since the sum of money triples itself in 3 years, the final amount after 3 years is 3P.

Therefore, the final amount after 't' years will be:

A = P * (1 + R/100)^t

As the sum of money multiplies five times, the final amount will be 5P.

Therefore, we have:

5P = P * (1 + R/100)^t

Simplifying the equation, we get:

(1 + R/100)^t = 5

Taking the logarithm on both sides, we have:

t * log(1 + R/100) = log(5)

Now, substituting the value of R, we have:

t * log(1 + 200/300) = log(5)
t * log(3/2) = log(5)

Dividing both sides by log(3/2), we get:

t = log(5) / log(3/2)

Using logarithmic properties, we can simplify the equation further:

t = log(5) / log(3) - log(2)

Calculating the values using a calculator, we find:

t ≈ 5.7 years

Therefore, the sum of money will multiply five times in approximately 5.7 years, which is closest to 6 years.

Hence, the correct answer is option D) 6 years.

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