The question states that a shopkeeper sold a book for ₹544 at a loss of 36%. We need to calculate the original cost price of the book and then determine the selling price required to earn a gain of 24%.
Identify the given information:
Calculate the cost price of the book:
Since the shopkeeper incurred a loss of 36%, the selling price represents 64% of the cost price.
\[ 100-36=64\% \]Using the formula:
\[ \text{Cost Price}=\frac{\text{Selling Price}\times100}{100-\text{Loss Percentage}} \]Substituting the given values:
\[ \text{Cost Price}=\frac{544\times100}{64} \] \[ =850 \]Therefore, the cost price of the book is ₹850.
Calculate the required gain:
The shopkeeper wants to earn a gain of 24% on the cost price.
\[ \text{Gain}=\frac{24}{100}\times850 \] \[ =204 \]Therefore, the required gain is ₹204.
Calculate the new selling price:
The new selling price is the sum of the cost price and the required gain.
\[ \text{New Selling Price}=\text{Cost Price}+\text{Gain} \] \[ =850+204 \] \[ =1054 \]Therefore, the book should be sold for ₹1,054 to earn a gain of 24%.
Correct Option: A) ₹1,054 — The book was originally sold for ₹544 at a loss of 36%, so its cost price is \(\frac{544\times100}{64}=850\). To earn a gain of 24%, the required selling price is \(850\times\frac{124}{100}=1054\). Hence, Option A is the correct answer.
B) ₹1,057: This is incorrect because selling the book for ₹1,057 would result in a gain of approximately 24.35%, not exactly 24%.
C) ₹1,056: This is incorrect because selling the book for ₹1,056 would result in a gain of approximately 24.24%, which is greater than the required 24%.
D) ₹1,055: This is incorrect because selling the book for ₹1,055 would result in a gain of approximately 24.12%, not exactly 24%.
This problem involves work and time. We need to find the individual work rate of B and then calculate the time B takes to complete half of the work. The key is to use the concept that the amount of work done is inversely proportional to the time taken, or that the work rate is the reciprocal of the time taken to complete the whole work.
A and B together complete the work in 14 days. So, their combined work rate is:
\[ \text{Work rate of (A + B)} = \frac{1}{14} \text{ work per day} \]A alone can do the work in 63 days. So, A's work rate is:
\[ \text{Work rate of A} = \frac{1}{63} \text{ work per day} \]The work rate of B can be found by subtracting A's work rate from the combined work rate of A and B:
\[ \text{Work rate of B} = \text{Work rate of (A + B)} - \text{Work rate of A} \]\[ \text{Work rate of B} = \frac{1}{14} - \frac{1}{63} \]To subtract these fractions, find a common denominator. The least common multiple (LCM) of 14 and 63 is 126.\[ \text{Work rate of B} = \frac{9}{126} - \frac{2}{126} \]\[ \text{Work rate of B} = \frac{9 - 2}{126} = \frac{7}{126} \]Simplify the fraction:\[ \text{Work rate of B} = \frac{1}{18} \text{ work per day} \]Since B's work rate is \(\frac{1}{18}\) work per day, B alone can complete the whole work in 18 days.
To complete half of the work, B will take half the time:
\[ \text{Time for B to do half work} = \frac{1}{2} \times \text{Time for B to do whole work} \]\[ \text{Time for B to do half work} = \frac{1}{2} \times 18 \text{ days} \]\[ \text{Time for B to do half work} = 9 \text{ days} \]Correct Option: A) 9
The question asks to identify the Buddhist architectural structure where relics of Buddha are typically enshrined. This requires knowledge of the different types of Buddhist architecture and their primary functions.
D) Stupas are hemispherical structures containing relics (bones, teeth, ashes) of the Buddha or his disciples, making them sacred sites for veneration and meditation. The relics are typically placed in a casket within the core of the stupa.
The diagonals of a rhombus are in the ratio 8 : 15, and the perimeter is 102 cm. Find the area (in cm2) of the rhombus.
To find the area of the rhombus, we need the lengths of its diagonals. We are given the ratio of the diagonals and the perimeter of the rhombus. We can use the properties of a rhombus (diagonals bisect each other at right angles, and all sides are equal) and the Pythagorean theorem to find the actual lengths of the diagonals and then calculate the area.
Define the diagonals and side length:
Let the diagonals be \(d_1\) and \(d_2\). Given their ratio is \(8:15\), we can write:
\[ d_1 = 8x \]\[ d_2 = 15x \]The perimeter of the rhombus is given as \(102 \text{ cm}\). Since all sides of a rhombus are equal, let the side length be \(a\).
\[ 4a = 102 \text{ cm} \]So, the side length \(a\) is:
\[ a = \frac{102}{4} = \frac{51}{2} = 25.5 \text{ cm} \]Apply the Pythagorean theorem:
The diagonals of a rhombus bisect each other at right angles. This forms four right-angled triangles inside the rhombus. The hypotenuse of each right-angled triangle is the side of the rhombus (\(a\)), and the legs are half the lengths of the diagonals (\(\frac{d_1}{2}\) and \(\frac{d_2}{2}\)).
Using the Pythagorean theorem:
\[ \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = a^2 \]Substitute the expressions for \(d_1\), \(d_2\), and \(a\):
\[ \left(\frac{8x}{2}\right)^2 + \left(\frac{15x}{2}\right)^2 = \left(\frac{51}{2}\right)^2 \]\[ (4x)^2 + \left(\frac{15x}{2}\right)^2 = \left(\frac{51}{2}\right)^2 \]\[ 16x^2 + \frac{225x^2}{4} = \frac{2601}{4} \]Solve for \(x\):
Multiply the entire equation by 4 to eliminate the denominators:
\[ 64x^2 + 225x^2 = 2601 \]\[ 289x^2 = 2601 \]\[ x^2 = \frac{2601}{289} \]We know that \(17^2 = 289\) and \(51^2 = 2601\). Also, \(51 = 3 \times 17\), so \(51^2 = (3 \times 17)^2 = 9 \times 17^2 = 9 \times 289 = 2601\).\[ x^2 = \frac{2601}{289} = 9 \]\[ x = \sqrt{9} = 3 \]Calculate the lengths of the diagonals:
\[ d_1 = 8x = 8 \times 3 = 24 \text{ cm} \]\[ d_2 = 15x = 15 \times 3 = 45 \text{ cm} \]Calculate the area of the rhombus:
The area of a rhombus is given by the formula:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]\[ \text{Area} = \frac{1}{2} \times 24 \times 45 \]\[ \text{Area} = 12 \times 45 \]\[ \text{Area} = 540 \text{ cm}^2 \]A) \(540 \text{ cm}^2\)
To find the average speed, we need to calculate the total distance traveled and the total time taken. The average speed is then the total distance divided by the total time.
Correct Option: A) 25
The problem asks us to identify numbers in a given series that are immediately preceded by a symbol and immediately followed by a symbol. We need to count how many such numbers exist by scanning the series from left to right.
1 \( @ % 1 4 3 * # 6 3 4 £ % 2 @ 6 % 8 % 9 \)D) 4. There are 4 such numbers (2, 6, 8, 9) that are immediately preceded by a symbol and immediately followed by a symbol.
If the roots of the quadratic equation kx2 − 4x + 1 = 0 are real and equal, what is the value of k?
To find the value of \(k\) for which the roots of a quadratic equation are real and equal, we use the discriminant property. For a quadratic equation in the form \(ax^2 + bx + c = 0\), the roots are real and equal if and only if its discriminant, \(\Delta = b^2 - 4ac\), is equal to zero.
B) 4 — When \(k=4\), the discriminant is zero, ensuring that the quadratic equation has real and equal roots.
The question asks to identify the Windows OS desktop element responsible for storing and allowing the restoration of deleted files and folders. We need to evaluate each given option based on its primary function in the Windows operating system.
C) Recycle Bin — The Recycle Bin is a special folder in Windows OS that temporarily stores files and folders that have been deleted by the user. This allows users to recover accidentally deleted items before they are permanently removed from the system. It is a fundamental feature for data recovery on a Windows desktop.
The question asks to identify the highest peak of the Maikal range. This requires knowledge of the major mountain ranges and their prominent peaks in India.
D) Amarkantak is the highest peak of the Maikal range. It is also a significant pilgrimage site and the source of several important rivers.
The question asks to identify the film director who received the Outstanding Achievement in Indian Cinema award at IIFA 2025. This is a factual question related to current affairs and awards in the Indian film industry.
Correct Option: C) Rakesh Roshan received the Outstanding Achievement in Indian Cinema award at IIFA 2025. He is a veteran director, producer, and actor known for his significant contributions to Hindi cinema, including films like 'Kaho Naa... Pyaar Hai', 'Koi... Mil Gaya', and the 'Krrish' series.