Question
An equal sum of money is invested in two schemes which
offer interest at the same rate but one at simple interest and the other at compound interest (compounded annually). Simple interest and compound interest received at the end of 2 years is Rs. 1,500 and Rs. 1,650, respectively. Find the rate of interest.Solution
ATQ, Let the sum invested in two schemes be Rs. 'P'. Let the rate of interest be 'r%', per annum. We know that, simple interest received at the end of each year of investment is equal. Simple interest received at the end of first year = Simple interest received at the end of second year = (1500/2) = Rs. 750 Also, simple interest and compound interest received at the end of first year are equal. So, simple interest received at the end of first year = Compound interest received at the end of first year = Rs. 750 Compound interest received in the second year = 1650 - 750 = Rs. 900 So, we can say that a sum of Rs. 750 amounts to Rs. 900 at the end of a year at the given rate of interest. Compound interest received for 1 year = Simple interest received for 1 year Simple interest = Principal X (Rate/100) X Time 750 X (r/100) X 1 = 900 - 750 So, r = 150 X (5/10) = 10 Therefore, rate of interest = r = 20%
The average of 11 observations is 60. If the average of first five observations is 58 and that of last five is 56, the sixth observation is
Average of 20 numbers is 90. Average of first 8 numbers is 92 while average of last nine numbers is 40. If ninth number is 25% less than the tenth numbe...
The income of B is 85% of A and income of C is Rs 3600 more than that of B. The average income of all three together is Rs. 8400. A and B spend 50% of t...
A player scored an average of 58 runs per match in the first 30 matches. In his next 10 matches, he scored runs with an average of ‘x’ runs per matc...
The average mark obtained by 140 candidates in a certain examination is 40. If the average marks of passed candidates are 55 and that of the failed cand...
The average number of books on history, polity and geography in a library is 110, and the average number of books on history and geography is 120. If th...
- The average of 9 scores is 45. If two new scores are added and their average is 'x', the overall average becomes 20% more than the previous average. Find t...
In an examination the average marks of Rohit is 55. If he got 15 more marks in science and 27 more marks in maths then his average would have been 61. F...
The average of 8 numbers is 5.95. The average of two of them is 5.4, while the average of the other two is 5.86. the average of the remaining four numbe...
If the average of two numbers is 20 and the square root of their product is 16, then the difference between the numbers is: