To solve this problem, we need to determine the selling price required to achieve an 8% gain and then calculate the discount percentage needed from the marked price. We will assume a cost price to make calculations easier.
Let the Cost Price (CP) of the item be \( \text{Rs. } 100 \).
The shopkeeper fixes the marked price 50% above its cost price.
\[ \text{MP} = \text{CP} + 50\% \text{ of CP} \]\[ \text{MP} = 100 + \frac{50}{100} \times 100 = 100 + 50 = \text{Rs. } 150 \]The shopkeeper wants to gain 8%.
\[ \text{SP} = \text{CP} + 8\% \text{ of CP} \]\[ \text{SP} = 100 + \frac{8}{100} \times 100 = 100 + 8 = \text{Rs. } 108 \]The discount is the difference between the Marked Price and the Selling Price.
\[ \text{Discount Amount} = \text{MP} - \text{SP} \]\[ \text{Discount Amount} = 150 - 108 = \text{Rs. } 42 \]The discount percentage is calculated on the Marked Price.
\[ \text{Discount Percentage} = \frac{\text{Discount Amount}}{\text{MP}} \times 100\% \]\[ \text{Discount Percentage} = \frac{42}{150} \times 100\% \]\[ \text{Discount Percentage} = \frac{42 \times 100}{150}\% \]\[ \text{Discount Percentage} = \frac{42 \times 2}{3}\% \]\[ \text{Discount Percentage} = 14 \times 2\% \]\[ \text{Discount Percentage} = 28\% \]Correct Option: C) 28%
A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/symbol | 9 | 7 | 6 | - | 8 | @ | # | + | 2 | % | ÷ | 3 | 1 | & |
| Code | C | R | J | Z | L | F | I | Y | Q | P | V | S | U | E |
Conditions:
If the fourth element is a number, then it is to be coded as γ.
If the first element is a multiple of 3, then it is to be coded as β.
If the second and the fifth elements are symbols, then the codes for these two (the second and the fifth elements) are to be interchanged.
What will be the code for the following group?
9 # @ 2 7
The problem requires us to code a given group of numbers and symbols based on a provided coding table and a set of conditions. We need to apply the conditions sequentially and then use the direct codes if no conditions apply.
Identify the given group: The group to be coded is 9 # @ 2 7.
List the direct codes from the table:
So, the initial code without applying conditions would be CIFQR.
Apply Condition 1: "If the fourth element is a number, then it is to be coded as \(\gamma\)."
The code becomes CI\(\gamma\)R.
Apply Condition 2: "If the first element is a multiple of 3, then it is to be coded as \(\beta\)."
The code becomes \(\beta\)I\(\gamma\)R.
Apply Condition 3: "If the second and the fifth elements are symbols, then the codes for these two (the second and the fifth elements) are to be interchanged."
Final Code: After applying all applicable conditions, the final code for 9 # @ 2 7 is \(\beta\)IF\(\gamma\)R.
D) \(\beta\)IF\(\gamma\)R — This matches our derived code after applying the conditions sequentially.
The mean proportional between 9 + 3\(\sqrt{7}\) and 18 − 6\(\sqrt{7}\) is:
The mean proportional (or geometric mean) between two numbers, say \(a\) and \(b\), is given by \(\sqrt{ab}\). We need to calculate this value for the given expressions \(9 + 3\sqrt{7}\) and \(18 - 6\sqrt{7}\).
Define the given numbers:
Let \(a = 9 + 3\sqrt{7}\)
Let \(b = 18 - 6\sqrt{7}\)
Recall the formula for mean proportional:
The mean proportional \(M\) between \(a\) and \(b\) is \(M = \sqrt{ab}\).
Calculate the product \(ab\):
\[ ab = (9 + 3\sqrt{7})(18 - 6\sqrt{7}) \]
Factor out common terms from each expression:
\[ a = 3(3 + \sqrt{7}) \]
\[ b = 6(3 - \sqrt{7}) \]
Now, multiply them:
\[ ab = [3(3 + \sqrt{7})][6(3 - \sqrt{7})] \]
\[ ab = 18(3 + \sqrt{7})(3 - \sqrt{7}) \]
Use the algebraic identity \((x+y)(x-y) = x^2 - y^2\):
\[ ab = 18(3^2 - (\sqrt{7})^2) \]
\[ ab = 18(9 - 7) \]
\[ ab = 18(2) \]
\[ ab = 36 \]
Calculate the mean proportional \(M\):
\[ M = \sqrt{ab} \]
\[ M = \sqrt{36} \]
\[ M = 6 \]
A) 6 is the correct answer because the product of the two given numbers is 36, and the square root of 36 is 6.
The question asks to identify the organization crucial for agricultural research and the dissemination of High-Yielding Variety (HYV) seeds during India's Green Revolution. This requires knowledge of the key institutions involved in agricultural development in India.
B) ICAR (Indian Council of Agricultural Research) played a pivotal role in the Green Revolution by conducting research, developing new crop varieties (including HYV seeds), and facilitating their dissemination to farmers across India. It was instrumental in providing the scientific and technical backbone for the agricultural transformation.
This problem involves calculating profit, marked price, and discount percentage. We will assume a cost price, then calculate the marked price based on the given markup percentage. Next, we will calculate the selling price using the given profit percentage. Finally, we will use the marked price and selling price to find the discount percentage (X).
Assume the Cost Price (CP):
Let the Cost Price (CP) of the goods be \(₹100\).
Calculate the Marked Price (MP):
The grocer marked his goods at 70% above the cost price.
\[ \text{Marked Price (MP)} = \text{CP} + (70\% \text{ of CP}) \] \[ \text{MP} = 100 + \left(\frac{70}{100} \times 100\right) \] \[ \text{MP} = 100 + 70 = ₹170 \]Calculate the Selling Price (SP) based on Profit:
He gained 53% profit.
\[ \text{Selling Price (SP)} = \text{CP} + (53\% \text{ of CP}) \] \[ \text{SP} = 100 + \left(\frac{53}{100} \times 100\right) \] \[ \text{SP} = 100 + 53 = ₹153 \]Calculate the Discount Percentage (X):
The goods were sold at a discount of X%. The discount is always calculated on the Marked Price.
\[ \text{Discount Amount} = \text{MP} - \text{SP} \] \[ \text{Discount Amount} = 170 - 153 = ₹17 \]Now, calculate the discount percentage (X):
\[ \text{Discount Percentage (X)} = \left(\frac{\text{Discount Amount}}{\text{Marked Price}}\right) \times 100\% \] \[ X = \left(\frac{17}{170}\right) \times 100\% \] \[ X = \left(\frac{1}{10}\right) \times 100\% \] \[ X = 10\% \]C) 10
The value of X, the discount percentage, is 10%.
This question tests general knowledge about contemporary literature and authors. To answer correctly, one needs to identify the author associated with the specified novel and its publication year.
Correct Option: C) Ocean Vuong is the author of the upcoming 2025 novel The Emperor of Gladness.
Sharad can complete a piece of work alone in 13 days and Varad can complete the same piece of work alone in 9 days. They started the work together, but Varad had to leave 11 days before the completion of the work. In how many days will the work be completed?
9 \( \frac{10}{11} \)
10 \( \frac{5}{11} \)
11 \( \frac{9}{11} \)
12 \( \frac{2}{11} \)
This problem involves work and time. We need to calculate the individual work rates, then consider the scenario where one person leaves before completion. We can solve this by calculating the total work using the LCM of the individual days, finding daily efficiencies, and then setting up an equation based on the work done.
C) 11 \( \frac{9}{11} \)
The total time taken to complete the work is \(11 \frac{9}{11}\) days, as calculated above.
Which Indian Constitutional Amendment Act states about the minimisation of inequalities in income, status, facilities and opportunities as a Directive Principle of State Policy?
44th Amendment Act of 1978
86th Amendment Act of 2002
42nd Amendment Act of 1976
97th Amendment Act of 2011
The question asks to identify the Constitutional Amendment Act that introduced the minimization of inequalities in income, status, facilities, and opportunities as a Directive Principle of State Policy. This requires knowledge of key amendments and their provisions related to Directive Principles.
A) 44th Amendment Act of 1978: This amendment added clause (2) to Article 38, explicitly directing the State to minimise inequalities in income, status, facilities, and opportunities. This was a significant step towards achieving social and economic justice.
We need to find the number of sides of a regular polygon given the difference between its interior and exterior angles. We will use the formulas for the interior and exterior angles of a regular polygon and the relationship between them.
Let \(n\) be the number of sides of the regular polygon.
The formula for the measure of an exterior angle of a regular polygon is:
\[ \text{Exterior Angle} = \frac{360^\circ}{n} \]The formula for the measure of an interior angle of a regular polygon is:
\[ \text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n} \]Alternatively, we know that the interior angle and exterior angle at any vertex of a polygon are supplementary (add up to \(180^\circ\)). So,
\[ \text{Interior Angle} + \text{Exterior Angle} = 180^\circ \]We are given that the difference between the interior angle and the exterior angle is \(140^\circ\):
\[ \text{Interior Angle} - \text{Exterior Angle} = 140^\circ \]We now have a system of two linear equations with two variables:
Equation (1): \(I + E = 180^\circ\)
Equation (2): \(I - E = 140^\circ\)
where \(I\) is the interior angle and \(E\) is the exterior angle.
Add Equation (1) and Equation (2):
\[ (I + E) + (I - E) = 180^\circ + 140^\circ \]\[ 2I = 320^\circ \]\[ I = \frac{320^\circ}{2} \]\[ I = 160^\circ \]Substitute the value of \(I\) into Equation (1) to find \(E\):
\[ 160^\circ + E = 180^\circ \]\[ E = 180^\circ - 160^\circ \]\[ E = 20^\circ \]Now, use the formula for the exterior angle to find the number of sides \(n\):
\[ E = \frac{360^\circ}{n} \]\[ 20^\circ = \frac{360^\circ}{n} \]\[ n = \frac{360^\circ}{20^\circ} \]\[ n = 18 \]Thus, the polygon has 18 sides.
C) 18. The number of sides of the regular polygon is 18, as calculated from the given conditions.