Question

ICICI lent Rs. 1 lakh to captain Ram Singh at \[6\% \] per annum of simple interest for 10 years period. Meanwhile ICICI offered a discount in rate of interest for armed forces. Thus the rate of interest ICICI decreased to \[4\% \]. In this way Ram Singh had to pay a total amount 1.48 lakh. After how many years Ram Singh got the discount in rate of interest?
A) 3 years
B) 4 years
C) 6 years
D) 5 years

Answer 1

Hint: Here in the given question based on simple interest, discount interest rates and time, it is basically a general aptitude question, this can be solved by using the concept of discount interest rates and further simplify using the basic mathematical operation. We get the required time or year which Ram Singh got the discount in rate of interest.

Complete step-by-step solution:
Consider the given data
ICICI lent 1 lakh or 1,00,000 rupees to Captain Ram Singh.
With simple interest \[6\% \] per annum for time period 10 years
Decreased rate of interest is \[4\% \]
The total amount paid by Ram Singh is 1.48 lakh.
Now we have to find after how many years Ram Singh got the discount in rate of interest.
Let's consider the discount was given after x years.
The total interest paid by Ram Singh is
\[ \Rightarrow \,\,\,148000 - 100000\]
\[ \Rightarrow \,\,\,48000\]Rs.
Now find the value of x, then
\[ \Rightarrow \,\,\,48000 = \left( {\dfrac{{100000}}{{100}}} \right)\left( {6x + 4\left( {10 - x} \right)} \right)\]
On simplifying, we get
\[ \Rightarrow \,\,\,48000 = 1000\left( {6x + 40 - 4x} \right)\]
\[ \Rightarrow \,\,\,48000 = 1000\left( {2x + 40} \right)\]
Take 1000 from RHS to LHS, then
\[ \Rightarrow \,\,\,\dfrac{{48000}}{{1000}} = 2x + 40\]
On simplification, we get
\[ \Rightarrow \,\,\,48 = 2x + 40\]
Isolate the constant term and take x to the LHS, then
\[ \Rightarrow \,\,\,2x = 48 - 40\]
\[ \Rightarrow \,\,\,2x = 8\]
Divide both side by 4, then
\[ \Rightarrow \,\,\,x = 4\]
Hence, after 4 years Ram Singh got the discount in rate of interest.

Therefore the correct answer is option ‘B’.

Note: The compound interest is interest calculated on the amount that includes principal and accumulated interest of the previous period whereas simple interest is interest on the invested amount for entire period. This is the difference between the simple interest and compound interest.