a sum of money amounts to Rs. 17680 when invested for 3years at a certain rate of interest per annum and amounts to Rs.17600 when invested for 2years. at the rate pf 5% per annum simple interest. find the rate of interest in the first investment and the sum invested in both the cases.
Answers
Answer:
Let :-
The sum of money be P
To Find :-
The rate of interest = ?
The sum invested = ?
Solution :-
To calculate rate of interest and sum invested at first we have to set up equation as per the given clue in question. Then solve the equation.
Calculation for Case - (i)
Amount = 17680 Rate = R%. Time = 3 years
⟼ A = P(1 + RT/100)
⟼ 17680 = P(1 + R × 3/100)
⟼ 17680 = P( 100 + 3R/100)--------(i)
Calculation for Case - (ii)
Amount = 17600. Rate = 5%. Time = 2 years
⟼ A = P(1 + RT/100)
⟼ 17600 = P(1 + 5×2/100)
⟼17600 = P(1 + 10/100)
⟼ 17600 = P(110/100)
⟼ 110P = 17600 × 100
⟼ P = 160 × 100
⟼ P = 16000
Now calculate Rate for Case - (i)
P = 16000. T = 3 years. Amount = 17680
⟼ A = P(1 + RT/100)
⟼ 17680 = 16000(1 + R × 3/100)
⟼ 17680/16000 = (100 + 3R)/100---------(i)
⟼ 16000(100 + 3R) = 17680 × 100
⟼ 16(100 + 3R) = 1768
⟼ 1600 + 48R = 1768
⟼ 48R = 1768 - 1600
⟼ 48R = 168
⟼ R = 3.5%
Hence,
The rate of interest (Case - (i)) = 3.5%
The sum invested in (Case - (i) and (ii)) = 16000
Step-by-step explanation: