On a certain sum, simple interest for \( \frac{5}{2} \) years at an annual rate of 12% is Rs 50 less than the interest on the same sum for \( \frac{7}{2} \) years at an annual rate of 10%. Find the sum.
We need to find the principal sum. We are given two scenarios for simple interest on the same sum, and the difference between the interests is Rs 50. We will use the formula for simple interest \(SI = \frac{P \times R \times T}{100}\) for both scenarios, set up an equation based on the given difference, and solve for the principal sum \(P\).
Let the principal sum be \(P\).
Scenario 1:
Scenario 2:
Formulate the equation:
The problem states that the interest in Scenario 1 is Rs 50 less than the interest in Scenario 2. Therefore:
\[ SI_2 - SI_1 = 50 \] \[ \frac{7P}{20} - \frac{3P}{10} = 50 \]Solve for \(P\):
To subtract the fractions, find a common denominator, which is 20.
\[ \frac{7P}{20} - \frac{3P \times 2}{10 \times 2} = 50 \] \[ \frac{7P}{20} - \frac{6P}{20} = 50 \] \[ \frac{7P - 6P}{20} = 50 \] \[ \frac{P}{20} = 50 \] \[ P = 50 \times 20 \] \[ P = 1000 \]The sum is Rs 1,000.
Correct Option: B) 1,000
The question asks for the ocean where the Ninety East Ridge is located. This requires knowledge of major submarine geographical features and their locations.
Correct Option: D) The Ninety East Ridge is a major submarine volcanic ridge located in the Indian Ocean. It extends for approximately 5,000 km from the Bay of Bengal in the north to the Southeast Indian Ridge in the south, running roughly along the 90° East longitude.
The period of an element in the Modern Periodic Table is determined by the number of electron shells (or energy levels) occupied by its electrons. The electronic configuration given (2, 8, 2) directly indicates the number of occupied shells.
B) 3 is the correct answer because the element has three occupied electron shells, and the number of occupied shells determines the period number.
This question tests the understanding of different forms of energy, particularly kinetic and potential energy, and their interconversion during the free fall of an object. The key is to analyze the state of the object just as it makes contact with the ground.
Correct Option: C) kinetic energy — Just at the time it touches the ground (i.e., just before impact), the object has reached its maximum velocity, and its height above the ground is practically zero. Therefore, all its initial potential energy has been converted into kinetic energy. It possesses maximum kinetic energy at this point.
The area of the circumcircle of a right-angled triangle whose sides are 6 cm, 8 cm and 10 cm will be:
To find the area of the circumcircle of a right-angled triangle, we first need to determine the radius of the circumcircle. For a right-angled triangle, the hypotenuse is the diameter of its circumcircle. Once the diameter is known, the radius can be calculated, and then the area of the circle can be found using the formula \(A = \pi r^2\).
Identify the sides of the right-angled triangle: The given sides are 6 cm, 8 cm, and 10 cm.
Verify if it's a right-angled triangle: We can use the Pythagorean theorem \(a^2 + b^2 = c^2\) to check. Here, \(6^2 + 8^2 = 36 + 64 = 100\) and \(10^2 = 100\). Since \(6^2 + 8^2 = 10^2\), it is indeed a right-angled triangle, and the hypotenuse is 10 cm.
Determine the diameter of the circumcircle: For any right-angled triangle, the hypotenuse is the diameter of its circumcircle. Therefore, the diameter \(D = 10\) cm.
Calculate the radius of the circumcircle: The radius \(r\) is half of the diameter.
\[ r = \frac{D}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm} \]Calculate the area of the circumcircle: The area \(A\) of a circle is given by the formula \(A = \pi r^2\).
\[ A = \pi (5 \text{ cm})^2 = \pi (25 \text{ cm}^2) = 25\pi \text{ cm}^2 \]B) \(25\pi \text{ cm}^2\) is the correct area of the circumcircle, as calculated.
This question tests knowledge about the chemical properties of milk and common household additives used to preserve food. The key is understanding why milk sours and how baking soda counteracts this process.
Correct Option: C) To prevent acidisation of milk
The problem involves calculating the cost price of an item given its selling price and a loss percentage, and then determining a new selling price to achieve a desired profit percentage. We will use the formulas for selling price with loss and selling price with profit.
Calculate the Cost Price (CP):
Given that the selling price (SP1) is Rs 48 and there is a loss of 20%.
The formula for selling price with loss is:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \]Substitute the given values:
\[ 48 = \text{CP} \times \left(1 - \frac{20}{100}\right) \] \[ 48 = \text{CP} \times \left(1 - 0.20\right) \] \[ 48 = \text{CP} \times 0.80 \]Now, solve for CP:
\[ \text{CP} = \frac{48}{0.80} \] \[ \text{CP} = \frac{480}{8} \] \[ \text{CP} = 60 \text{ Rs} \]So, the cost price of the jute bag is Rs 60.
Calculate the new Selling Price (SP2) for a 20% profit:
We want to make a profit of 20% on the cost price (CP = Rs 60).
The formula for selling price with profit is:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]Substitute the values:
\[ \text{SP2} = 60 \times \left(1 + \frac{20}{100}\right) \] \[ \text{SP2} = 60 \times \left(1 + 0.20\right) \] \[ \text{SP2} = 60 \times 1.20 \] \[ \text{SP2} = 72 \text{ Rs} \]Therefore, to make a profit of 20%, the selling price of the jute bag should be Rs 72.
B) Rs 72 is the correct selling price to achieve a 20% profit after determining the cost price from the initial loss scenario.
To find the molecular mass of a compound, we need to sum the atomic masses of all the atoms present in its molecule. For diatomic molecules like O₂, this involves multiplying the atomic mass of the element by the number of atoms in the molecule.
Therefore, the molecular mass of O₂ is \(32\).
Correct Option: C) 32
The question asks about the field for which Sadhguru Jaggi Vasudev received the Padma Vibhushan in 2017. This requires knowledge of prominent personalities and their contributions recognized by national awards.
Correct Option: C) Spirituality
This problem involves calculating the percentage decrease in quantity when there's an increase in price and a limited increase in expenditure. We can solve this by assuming initial values for price and quantity, then calculating the new values based on the given percentages, and finally finding the percentage change in quantity.
Let the initial cost of tomatoes be \( \text{₹}100 \) per kg.
Let the initial quantity of tomatoes Sudha buys be \( 100 \) kg.
Therefore, the initial expenditure is:
\[ \text{Initial Expenditure} = \text{Initial Cost} \times \text{Initial Quantity} = \text{₹}100 \times 100 \text{ kg} = \text{₹}10,000 \]The cost of tomatoes increases by 25%.
\[ \text{New Cost} = \text{Initial Cost} + 25\% \text{ of Initial Cost} \]\[ \text{New Cost} = \text{₹}100 + (0.25 \times \text{₹}100) = \text{₹}100 + \text{₹}25 = \text{₹}125 \text{ per kg} \]Sudha wants to spend only 15% more on tomatoes.
\[ \text{New Expenditure} = \text{Initial Expenditure} + 15\% \text{ of Initial Expenditure} \]\[ \text{New Expenditure} = \text{₹}10,000 + (0.15 \times \text{₹}10,000) = \text{₹}10,000 + \text{₹}1,500 = \text{₹}11,500 \]Using the new expenditure and new cost per kg:
\[ \text{New Quantity} = \frac{\text{New Expenditure}}{\text{New Cost per kg}} \]\[ \text{New Quantity} = \frac{\text{₹}11,500}{\text{₹}125 \text{ per kg}} = 92 \text{ kg} \]The initial quantity was \( 100 \) kg and the new quantity is \( 92 \) kg.
\[ \text{Decrease in Quantity} = \text{Initial Quantity} - \text{New Quantity} = 100 \text{ kg} - 92 \text{ kg} = 8 \text{ kg} \]\[ \text{Percentage Decrease} = \frac{\text{Decrease in Quantity}}{\text{Initial Quantity}} \times 100\% \]\[ \text{Percentage Decrease} = \frac{8 \text{ kg}}{100 \text{ kg}} \times 100\% = 8\% \]Correct Option: B) 8%