Priya and khushi invested Rs.3000 together. Priya invested her amount at compound interest for ‘x/10’ years at x% rate interest and khushi invested half of her amount at compound interest and remaining half at simple interest at the same rate of interest for the same time period. [It is given that ‘x/10’ is a natural number] What is the value of ‘x’? Statement I: Ratio of investment of priya and khushi is 1 : 2 respectively and total sum received by them together after a particular time at x% rate of interest is Rs. 4280. Statement II: Simple interest received by khushi is Rs. 40 less than compound interest received by her. Statement III: Sum of simple interest and compound interest received by khushi after a certain time at x% rate of interest is Rs. 2500 Which of the above statement is redundant to find the answer of the given question? Correct Answer None of These Let investment of Khushi = p Investment of priya = 3000 – p Time = x/10 years Interest rate = x% For priya : CI = (3000 – p) × ((1 + (x/100))(x/10) – 1) For khushi : CI = (p/2) × ((1 + (x/100))(x/10) – 1) SI = (p/2) × x × (x/10)/100 = x2p/2000 Solution: Statement I: Let the time be ‘t’ years. Investment of khushi = p = (2/3) × 3000 = 2000 Investment of priya = 3000 – p = 3000 – 2000 = 1000 For priya: CI = 1000 × ((1 + (x/100))(t) -1) For khushi: CI = 1000 × ((1 + (x/100))(t) -1) SI = 1000 × x × (t)/100 = 10xt Total sum received by them together after given ‘t’ years = Rs 4280 4280 – 3000 = 1000 × ((1 + (x/100))(t) – 1) + 1000 × ((1 + (x/100))(t) -1) + 10xt From the above equation, Value of ‘x’ can’t be determined as there are 2 variable and one equation. Statement II: For Khushi: CI – SI = 40 CI = (p/2) × ((1 + (x/100))(x/10) – 1) SI = (p/2) × x × (x/10)/100 40 = (p/2) Value of ‘x’ cannot be determine by the above equation. Statement III: For khushi: Let the time be ‘n’ years. SI + CI = 2500 CI = (p/2) × (( 1 + (x/100))n – 1) SI = (p/2) × x × n/100 2500 = (p/2) × x × n/100 + (p/2) × ((1 + (x/100))n– 1) So, value of ‘x’ can’t be determine by the above equation. On combining I, II and III : There are three equation with four unknown variation. So the value of ‘x’ can’t be determined.