Directions: The following question is accompanied by three statements

1.	Directions: The following question is accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions.Find the principal amount.Statement I: The compound interest obtained when a sum is invested at 25% rate for 2 years is Rs. 250 more than the simple interest obtained when the same amount is invested at a 5% rate for 1 year.Statement II: A sum gets two more than its triple when it is invested at 3.5% rate compounded annually.Statement III: The difference of amount on a sum invested at 8% rate compounded annually and semi-annually is Rs. 279.1. The data in statement I alone is sufficient to answer the question, while the data in statement II and statement III alone are not sufficient to answer the question.2. The data in statement II alone is sufficient to answer the question, while the data in statement I and III is not sufficient to answer the question.3. The data in statement I alone or in statement II alone is sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.4. The data in all the statements I, II and III is not sufficient to answer the question.5. The data in statements I and statement II are sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.
Answer» Correct Answer - Option 1 : The data in statement I alone is sufficient to answer the question, while the data in statement II and statement III alone are not sufficient to answer the question. Formula used: SI = (P × R × T)/100 Amount = P × (1 + R/100)^t CI = P × [(1 + R/100)t- 1] where, SI → Simple interest, CI → Comp[und interest P → Principal, R → Rate of interest, T → Time period Calculations: Statement I: Let the principal amount be P. CI at 25% for 2 years = P × [(1 + 25/100)2- 1] ----(1) SI at 5% rate for 1 year = (P × 5 × 1)/100 ----(2) Now, (1) - (2) = Rs. 250 ⇒ 11P/16 - P/20 = Rs. 250 ⇒ 51P/80 = Rs. 250 ⇒ P = Rs. 20000/51 So, statement I is sufficient to answer the question. Statement II: Let the principal be P. ⇒ (3P + 2) = P × (1 + 3.5/100)t Since we have 1 equation 2 variables So it cannot be solved So, statement II is not sufficient to answer the question. Statement III: CI at 8% annually = P × [(1 + 8/100)t- 1] CI at 8% semi-annually = P × [(1 + (8//2)100)t- 1] P × [(1 + 8/100)t- 1] - P × [(1 + (8//2)100)t- 1] = Rs. 279 Since we have 1 equation 2 variables So it cannot be solved So, statement III is not sufficient to answer the question. ∴ The data in statement I alone is sufficient to answer the question, while the data in statement II and statement III alone are not sufficient to answer the question.

Directions: The following question is accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions.Find the principal amount.Statement I: The compound interest obtained when a sum is invested at 25% rate for 2 years is Rs. 250 more than the simple interest obtained when the same amount is invested at a 5% rate for 1 year.Statement II: A sum gets two more than its triple when it is invested at 3.5% rate compounded annually.Statement III: The difference of amount on a sum invested at 8% rate compounded annually and semi-annually is Rs. 279.1. The data in statement I alone is sufficient to answer the question, while the data in statement II and statement III alone are not sufficient to answer the question.2. The data in statement II alone is sufficient to answer the question, while the data in statement I and III is not sufficient to answer the question.3. The data in statement I alone or in statement II alone is sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.4. The data in all the statements I, II and III is not sufficient to answer the question.5. The data in statements I and statement II are sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.

Answer» Correct Answer - Option 1 : The data in statement I alone is sufficient to answer the question, while the data in statement II and statement III alone are not sufficient to answer the question.

Formula used:

SI = (P × R × T)/100

Amount = P × (1 + R/100)^t

CI = P × [(1 + R/100)t- 1]

where, SI → Simple interest, CI → Comp[und interest

P → Principal, R → Rate of interest, T → Time period

Calculations:

Statement I:

Let the principal amount be P.

CI at 25% for 2 years = P × [(1 + 25/100)2- 1] ----(1)

SI at 5% rate for 1 year = (P × 5 × 1)/100 ----(2)

Now, (1) - (2) = Rs. 250

⇒ 11P/16 - P/20 = Rs. 250

⇒ 51P/80 = Rs. 250

⇒ P = Rs. 20000/51

So, statement I is sufficient to answer the question.

Statement II:

Let the principal be P.

⇒ (3P + 2) = P × (1 + 3.5/100)t

Since we have 1 equation 2 variables

So it cannot be solved

So, statement II is not sufficient to answer the question.

Statement III:

CI at 8% annually = P × [(1 + 8/100)t- 1]

CI at 8% semi-annually = P × [(1 + (8//2)100)t- 1]

P × [(1 + 8/100)t- 1] - P × [(1 + (8//2)100)t- 1] = Rs. 279

Since we have 1 equation 2 variables

So it cannot be solved

So, statement III is not sufficient to answer the question.

∴ The data in statement I alone is sufficient to answer the question, while the data in statement II and statement III alone are not sufficient to answer the question.

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