A certain sum of money at simple interest becomes rs. 1062 in 2 years and rs. 1183.50 in 3½ years. what is rate of interest per annum? op 1: 7% op 2: 6% op 3: 9% op 4: 5%
Answers
Answer: 9%
Explanation: Let the certain sum of money be x.
The amount received in 2 years = Rs. 1,062
The amount received in 3.5 years = Rs. 1,183.5
The difference between the amount received in 2 years and 3.5 years is the interest amount for 1.5 years (3.5 years - 2 years), since it is simple interest.
Difference = Amount received in 3.5 years - Amount received in 2 years
Difference = Rs. 1,183.5 - Rs. 1,062
Difference = Rs. 121.50
Interest earned per annum = Difference in the amount / Difference in the number of years
Interest earned per annum = Rs. 121.50 / 1.50
Interest earned per annum = Rs. 81
Amount invested = Rs. 1,062 - (Rs. 81 * 2)
Amount Invested = Rs. 1062 - Rs. 162
Amount Invested = Rs. 900
Rate of Interest = Interest per annum / Amount Invested
Rate of Interest = Rs. 81 / Rs. 900 * 100
Rate of Interest = 9%
Therefore, the option is C (9%).
Let the amount of money =P.
SI= PXRXT/100 and Amount = P+ SI
1062 = P+ {PXRX2/100}------1
1183.50 ={ P+ PXRX3.5/100}-----2
Subrtacting 1 from 2 we get,
121.50= PXRX3.5/100-PXRX2/100
121.50= 3/2 X PXR/100
121.50X 200/3= PR
40.5x200=PR------3
8100= PR
Putting PR in 1 we get,
1062= P+8100x2/100
1062-162=P
900=P
Putting the value of P= 900 in 3 we get,
900xR= 40.5
R= 9.
Thus, the rate of Interest is 9%.