Question

: Rs. 1500 is invested at a rate of 10% simple interest and interest is added to the principal after every 5 years. In how many years will it amount to Rs. 2500?
(A) \[6\dfrac{1}{9}years\]
(B) \[6\dfrac{1}{4}years\]
(C) \[7years\]
(D)\[6years\]

Answer 1

Hint: According to the question, firstly find the simple interest for first 5 years using the given values and substitute them in the formula (S.I) = \[\dfrac{{P \times R \times T}}{{100}}\] . Then, find out the new principal and calculate how many years it will amount to Rs.2500 using formula amount = \[P + S.I\].

Formula used:
Here, we used the formula of simple interest (S.I) = \[\dfrac{{P \times R \times T}}{{100}}\] and amount = \[P + S.I\]

Complete step-by-step answer:
It is given that Rs.1500 is invested at a rate of 10% simple interest and interest is added to the principal after every 5 years.
Let P be the principal = Rs.1500, R be the rate = 10% and T be the time = 5years
Now, we will calculate Simple interest for the first 5 years using the formula S.I = \[\dfrac{{P \times R \times T}}{{100}}\]
So, substituting all the values of P, R and T in the formula.
We get, S.I = \[\dfrac{{1500 \times 10 \times 5}}{{100}}\]
\[ \Rightarrow \dfrac{{75000}}{{100}}\]
On dividing we get,
S.I = \[750Rs.\]
Then, the principal for the next 5 years is = Rs. \[\left( {1500 + 750} \right)\]
So, the principal = Rs 2250
As, the required amount = Rs.2500
And let the invested amount be Rs. 2500 in x years.
So, Amount = \[P + S.I\]
Here, we will calculate simple interest using formula S.I = \[\dfrac{{P \times R \times T}}{{100}}\] and by taking a new principal.
Substituting all the values of amount, P and R in the formula.
Hence, we calculate the value of x years.
$\Rightarrow$ \[2500 = 2250 + \dfrac{{2250 \times 10 \times x}}{{100}}\]
On simplifying we get,
$\Rightarrow$ \[2500 - 2250 = \dfrac{{2250 \times 10 \times x}}{{100}}\]
So, \[250 = \dfrac{{2250 \times 10 \times x}}{{100}}\]
Taking 100 on the left side.
$\Rightarrow$ \[25000 = 2250 \times 10 \times x\]
$\Rightarrow$ \[25000 = 22500x\]
Taking \[22500\] on the left hand side.
So, we get \[\dfrac{{25000}}{{22500}} = x\]
Cancelling zeroes from both numerator and denominator we get:
$\Rightarrow$ \[\dfrac{{250}}{{225}} = x\]
Dividing by 25 from both numerator and denominator.
Therefore, x comes out to be \[\dfrac{{10}}{9} = x\]
Thus, the total time required = \[5 + \dfrac{{10}}{9}\] years
On taking L.C.M we get,
\[ \Rightarrow \dfrac{{45 + 10}}{9}\] Years
\[ \Rightarrow \dfrac{{55}}{9}\] Converting them into mixed fractions.
\[ \Rightarrow 6\dfrac{1}{9}\] Years
Hence, option (A) \[6\dfrac{1}{9}years\] is correct.

Note: To solve these types of questions, you need to calculate simple interest using the given information. Then, step by step calculate the requirements to reach the solution and substitute the value in the formula.