Question

A sum of money becomes three times of itself in 10 years. In how many years will it become ten times of itself?​

Answer 1

Answer :-

• In 45 years it will become ten times of itself.

Step-by-step-Explaination :-

Step 1 :-

First Understand :-

See , here a sum of money will become 3 times the Principal also , time is given which is 10 years . Then how many years will it become ten times of it . So,

Step 2 :-

Assume the Principal and Amount or given :-

• Let the Principal be Rs x
• Then , Amount be Rs 3x
• Time is 10 years.

Then , from this information we can easily find Simple Interest (S.I) .

Hence ,

$\boxed{ \rm \: S.I = Amount - Principal } \bigstar$

Finding Simple Interest,

$\rm \: S.I = 3x - x$

$\rm \: S.I = 2x$

Also now we get to know ,

• Principal = x .
• Simple interest = 2x .
• Time = 10 years .

Now , from the above information we can easily find out the rate of interest.

$\rm \therefore\: Rate \: of \: interest \: = \dfrac{S.I \times 100}{principal \times time} \%p.a.$

$\rm \: Rate \: of \: interest \: = \cancel \dfrac{2x \times 100}{x \times 10} \%p.a.$

$\rm \bf \: Rate \: of \: interest \: = 20 \: \%p.a.$

Also now we get to know ,

• Principal = Rs . x
• Amount = Rs. 10x
• Rate of interest = 20% p.a.

Here , find out Simple Interest now ,

$\rm S.I = Rs.10x -Rs. x =\bf\:Rs. 9x$

Now , just simply find out the Time .

$\rm \therefore\: Time \: = \dfrac{S.I \times 100}{principal \times Rate \:of\: interest}$

$\rm \therefore\: Time \: = \cancel \dfrac{9x \times 100}{x \times 20}$

$\rm \therefore\: \bf Time \: = \underline{45 \: years}$

∴ It will take 45 years to become 10 times of itself.

Additional Information :

$\rm\bf \:\bigstar S.I = \dfrac{ Principal \times Time \times Rate \: of \: interest }{100}$

$\rm \bf\:\bigstar Principal = \dfrac{ S.I \times 100 }{ Time \times Rate \: of \: interest }$

$\rm \bf \:\bigstar Rate \: of \: interest \: = \dfrac{S.I \times 100}{principal \times Time} \%p.a.$

$\rm \bf \bigstar\: Time \: = \dfrac{S.I \times 100}{principal \times Rate \:of\: interest}$

$\rm \: \bf \bigstar\: Amount = Principal + interest$

Shortcuts :-

• Principal = P
• Amount = A
• Simple Interest = S.I
• Rate of interest = R
• Time = T

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

A sum of money becomes three times of itself in 10 years.

Let assume that

Sum of money invested, be Rs P

So,

Amount received after 10 years be Rs 3P

We know,

$\boxed{\sf{  \:\rm \: SI \: = \: Amount \: - \: Principal \: }}$

So, Simple interest received after 10 years given by

$\rm \: SI \: = \: 3P - P = 2P$

So, we have now

Principal = Rs P

Simple interest, SI = 2P

Time, n = 10 years

Let assume that the rate of interest be r % per annum.

We know,

Simple interest (SI) received on a certain sum of money of Rs P invested at the rate of r % per annum for n years is given by

$\boxed{\sf{  \:\rm \: SI = \dfrac{P \times r \times n}{100} \: \: }}$

So, on substituting the values, we get

$\rm \: 2P \: =  \: \dfrac{P \times \: r \times 10}{100}$

$\rm \: 2 \: =  \: \dfrac{ \: r \: }{10}$

$\rm\implies \:r \: = \: 20 \: \% \: per \: annum$

Now, we have to find after how many years it will become 10 times of itself.

So, we have

Principal = Rs P

Rate of interest, r = 20 % per annum

Amount = 10 P

Let assume that time taken be n years.

So,

$\rm \: SI \: = \: 10P - P = 9P$

Now, we know,

$\boxed{\sf{  \:\rm \: SI = \dfrac{P \times r \times n}{100} \: \: }}$

So, on substituting the values, we get

$\rm \: 9P \: = \: \dfrac{P \times 20 \times n}{100}$

$\rm \: 9 \: = \: \dfrac{n}{5}$

$\rm\implies \:n \: = \: 45 \: years$

So, it will take 45 years for the sum to be 10 times of itself.

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Additional Information :-

If Simple interest (SI) is received on a certain sum of money of Rs P invested at the rate of r % per annum for n years, then

$\boxed{\sf{  \:\rm \: r \: = \: \frac{SI \times 100}{P \times n} \: \: }}$

$\boxed{\sf{  \:\rm \: n\: = \: \frac{SI \times 100}{P \times n} \: \: }}$

$\boxed{\sf{  \:\rm \: P\: = \: \frac{SI \times 100}{r \times n} \: \: }}$

$\boxed{\sf{  \:\rm \: Amount = P\bigg[\dfrac{100 + rn}{100} \bigg] \: \: }}$