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Each of the questions below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question.Priya and khushi invested Rs.3000 together. Priya invested her amount at compound interest for ‘v/10’ years at v% 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 ‘v/10’ is a natural number]What amount is received by Khushi after ‘v/10’ years?Statement I: Value of ‘v’ can be determined by the equation : 3v2 – 55v - 100 = 0.Statement II: Priya invested Rs. 1000 less than amount invested by Khushi.Statement III: Total sum received Priya and Khushi together after ‘v/10’ years is Rs. 4280.1. Only statement I and II together are sufficient.2. Only statement I and III together are sufficient.3. Only statement II and III together are sufficient.4. Either statement I or III is sufficient alone.5. Statement I and either statement II or III together are sufficient. |
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Answer» Correct Answer - Option 5 : Statement I and either statement II or III together are sufficient. Let investment of Khushi = p Investment of priya = 3000 – p Time = v/10 years Tare = v% For priya: CI = (3000 – p) × ((1 + (v/100))(v/10) – 1) For khushi : CI = (p/2) × ((1 + (v/100))(v/10) – 1) SI = (p/2) × v × (v/10)/100 = v2p/2000 statement I: 3v2 – 55v – 100 = 0 3v2 – 60v + 5v – 100 = 0 V = 20, -1.67 For Khushi : CI = (p/2) × ((1 + (v/100))(v/10) – 1) CI = (p/2) × ((1 + (20/100))(20/10) – 1) = 11p/50 SI = v2p/2000 = 20 × 20 × p/2000 = p/5 statement II : 3000 -p = p - 1000 p = 2000 Statement III: 4280 = (3000 – p) × ((1 + (v/100))(v/10) – 1) + (p/2) × ((1 + (v/100))(v/10) – 1) + v2p/2000 From statement I and II : P = 2000 SI = p/5 = 2000/5 = Rs 400 CI = 11p/50 = 11 × 2000/50 = Rs 440 Total amount received by Khushi after (v/10) Years = 2000 + 400 + 440 = Rs 2840 Statement II and III: p = 2000 4280 = (3000 – 2000) × ((1 + (v/100))(v/10) – 1) + (2000/2) × ((1 + (v/100))(v/10) – 1) + v2 × 2000/2000 4280 = 2000 × ((1 + (v/100))(v/10) – 1) + v2 Value of ‘v’ cannot be determined. Hence, statement II and III together are not sufficient. From I and III: v = 20 For Priya : CI = (3000 – p) × ((1 + (20/100))(20/10) – 1) = (3000 – p) × 11/25 For Khushi : CI = 11p/50 SI = p/5 4280 - 3000 = (3000 – p) × (11/25) + (11p/50) + (p/5) P = Rs 2000 For Khushi : SI = p/5 = 2000/5 = Rs. 400 Total amount received by Khushi after (v/10) Years = 2000 + 400 + 440 = 2840 Hence, either statement II or III and statement I together are sufficient. |
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