We are given the compound interest (CI) for a certain sum, rate, and time. We need to find the simple interest (SI) for the same sum, rate, and time. We can use the formula for compound interest to find the principal amount, and then use the principal amount to calculate the simple interest.
Let the Principal be \(P\), Rate of Interest be \(R\), and Time be \(T\).
Given:
The formula for the Amount (\(A\)) under compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]The formula for Compound Interest (\(\text{CI}\)) is:
\[ \text{CI} = A - P = P \left(1 + \frac{R}{100}\right)^T - P \]\[ \text{CI} = P \left[ \left(1 + \frac{R}{100}\right)^T - 1 \right] \]Substitute the given values into the CI formula:
\[ 6305 = P \left[ \left(1 + \frac{5}{100}\right)^3 - 1 \right] \]\[ 6305 = P \left[ \left(1 + 0.05\right)^3 - 1 \right] \]\[ 6305 = P \left[ (1.05)^3 - 1 \right] \]Calculate \((1.05)^3\):
\[ (1.05)^3 = 1.05 \times 1.05 \times 1.05 = 1.157625 \]Substitute this value back into the equation:
\[ 6305 = P [1.157625 - 1] \]\[ 6305 = P [0.157625] \]Solve for \(P\):
\[ P = \frac{6305}{0.157625} \]\[ P = 40000 \]Now that we have the Principal \(P = \text{₹}40,000\), we can calculate the Simple Interest (\(\text{SI}\)) for the same sum, rate, and time.
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]Substitute the values:
\[ \text{SI} = \frac{40000 \times 5 \times 3}{100} \]\[ \text{SI} = \frac{600000}{100} \]\[ \text{SI} = 6000 \]The simple interest is ₹6,000.
A) 6,000/- is the correct simple interest calculated based on the principal derived from the given compound interest.
Which is the smallest fraction among the following fractions? \(\frac{3}{9}, \frac{8}{14}, \frac{5}{8}, \frac{4}{9}\)
\( \frac{8}{14} \)
\( \frac{5}{8} \)
\( \frac{4}{9} \)
\( \frac{3}{9} \)
To find the smallest fraction among a given set, we can convert all fractions to a common decimal form or find a common denominator to compare their numerators. Converting to decimal form is often the most straightforward method.
Now we have the decimal values:
Comparing these values, \( 0.333 \) is the smallest.
The fraction corresponding to \( 0.333 \) is \( \frac{3}{9} \).
Correct Option: D) \( \frac{3}{9} \)
The value of sin45°sec45°tan45° + cos60°sin30°sin90° − 4cos60° is:
-\( \frac{5}{4} \)
\( \frac{5}{4} \)
-\( \frac{3}{4} \)
\( \frac{3}{4} \)
To solve this problem, we need to recall the standard trigonometric values for common angles (0°, 30°, 45°, 60°, 90°). We will substitute these values into the given expression and then perform the arithmetic operations to find the final result.
Correct Option: C) \( -\frac{3}{4} \)
The question asks to find a term that relates to 'Wood' in the same way 'Silver' relates to 'Metal'. This is an analogy question where we need to identify the relationship between the first pair of words and apply the same relationship to the second pair.
Therefore, the relationship is Category : Specific Example.
Metal : Silver :: Wood : Teak
D) Teak is a specific type of wood, just as Silver is a specific type of metal. This maintains the same relationship.
This question tests general knowledge about major international sporting events. Specifically, it asks about the host city for the upcoming 2024 Summer Olympics. Recalling the host cities of recent and upcoming Olympic Games is key to answering this question.
Correct Option: A) Paris
The question asks to identify India's first hydroelectric plant. This requires knowledge of the history of power generation in India.
Correct Option: A) Sidrapong Hydroelectric Power Station
The Sidrapong Hydroelectric Power Station, located near Darjeeling in West Bengal, was commissioned in 1897. It holds the distinction of being India's first hydroelectric power plant, marking a significant milestone in the country's energy sector.
The question asks for the location of the Institute of Road Traffic Education (IRTE) in India. This is a factual question requiring knowledge of the geographical location of this specific institution.
Correct Option: C) Faridabad
The question asks for the year when the Simon Commission was appointed. This is a factual question related to Indian history, specifically the British Raj period. Recalling the key events and their timelines is crucial.
Correct Option: A) 1927
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Correct Option: D) NCLT
The question asks for the Indian state where the Central Institute of Indian Languages (CIIL) is located. This is a factual question requiring knowledge of the location of prominent national institutions.
Correct Option: B) The Central Institute of Indian Languages (CIIL) is located in Mysuru, Karnataka. It was established in 1969 with the objective of developing Indian languages through research, documentation, and training.