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Find the time taken for Rs. 400 to amount to Rs. 448 at the rate of 4% per annum.

Last updated date: 29th Feb 2024
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IVSAT 2024
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Hint: We need to apply the formula of Simple Interest and then put in the already given values and thus find the Interest. After that, add the Principal amount and Interest and equate it to Final Amount.

Complete step-by-step answer:
First, we have Principal Amount = P = Rs. 400
Final Amount = A = Rs. 448
Rate of Interest = R = 4%
We will use the formula of Simple Interest that is S.I. = \[\dfrac{{P \times R \times T}}{{100}}\], where
S.I. = Simple Interest, P = Principal Amount, R = Rate on Interest, T = Time taken in years
Now, we will put in the values of P and R in the formula for S.I.
So, S.I. = \[\dfrac{{400 \times 4 \times T}}{{100}}\]
Now simplify the value by eliminating 100 from the denominator. We get:-
S.I. = \[4 \times 4 \times T = 16T\]
We will now use the formula for Final amount which states that:-
Final amount = Principal amount + Interest that is A = P + S.I.
We will now put the values of P, S.I. and A.
So, 448= 400+ 16T
This is equivalent to writing:- 16T + 400 = 448
Now, we will take 400 to R.H.S
16T = 448 - 400 = 48
We will now take 16 from 16T to R.H.S
So, we get \[T = \dfrac{{48}}{{16}} = 3\]
Hence, the time taken will be 3 years.

Note: Remember both the formulas used in the solution S.I. = \[\dfrac{{P \times R \times T}}{{100}}\] and
Final amount = Principal amount + Interest. Always remember the units of all the variables. Sometimes, the question may ask for time in months as well, so we will then need to convert years into months or vice-versa.

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