To find Ramesh's gain, we need to calculate the interest he pays when borrowing the money and the interest he receives when lending it. The difference between the interest received and the interest paid will be his gain.
Ramesh borrows ₹8,000 at 5% p.a. for 3 years.
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \]Here, Principal (\(P\)) = ₹8,000, Rate (\(R\)) = 5%, Time (\(T\)) = 3 years.
\[ \text{SI}_{\text{paid}} = \frac{8000 \times 5 \times 3}{100} = \frac{120000}{100} = \text{₹}1200 \]Ramesh lends the same ₹8,000 to Manohar at 7% p.a. for 3 years.
Here, Principal (\(P\)) = ₹8,000, Rate (\(R\)) = 7%, Time (\(T\)) = 3 years.
\[ \text{SI}_{\text{received}} = \frac{8000 \times 7 \times 3}{100} = \frac{168000}{100} = \text{₹}1680 \]Ramesh's gain is the difference between the interest he receives and the interest he pays.
\[ \text{Gain} = \text{SI}_{\text{received}} - \text{SI}_{\text{paid}} \]\[ \text{Gain} = \text{₹}1680 - \text{₹}1200 = \text{₹}480 \]
Correct Option: B) ₹480 is the gain Ramesh makes from this transaction.
We are given a circle with center O, and two tangents PA and PB drawn from an external point P. We are given the angle \(\angle PAB = 55^\circ\) and need to find \(\angle AOB\). We will use properties of tangents, radii, and quadrilaterals to solve this problem.
Understand the properties of tangents: A tangent to a circle is perpendicular to the radius at the point of tangency. Therefore, \(OA \perp PA\) and \(OB \perp PB\).
This implies that \(\angle OAP = 90^\circ\) and \(\angle OBP = 90^\circ\).
Analyze \(\triangle PAB\): Since tangents from an external point to a circle are equal in length, \(PA = PB\). This means \(\triangle PAB\) is an isosceles triangle.
In an isosceles triangle, the angles opposite to the equal sides are equal. So, \(\angle PBA = \angle PAB\).
Given \(\angle PAB = 55^\circ\), we have \(\angle PBA = 55^\circ\).
Find \(\angle APB\): The sum of angles in a triangle is \(180^\circ\). In \(\triangle PAB\):
\[ \angle APB + \angle PAB + \angle PBA = 180^\circ \]\[ \angle APB + 55^\circ + 55^\circ = 180^\circ \]\[ \angle APB + 110^\circ = 180^\circ \]\[ \angle APB = 180^\circ - 110^\circ = 70^\circ \]Consider quadrilateral OAPB: The sum of angles in a quadrilateral is \(360^\circ\). In quadrilateral OAPB:
\[ \angle OAP + \angle APB + \angle PBO + \angle BOA = 360^\circ \]\[ 90^\circ + 70^\circ + 90^\circ + \angle BOA = 360^\circ \]\[ 250^\circ + \angle BOA = 360^\circ \]\[ \angle BOA = 360^\circ - 250^\circ = 110^\circ \]C) \(110^\circ\) is the correct answer. The angle \(\angle AOB\) is found to be \(110^\circ\) by using the properties of tangents and the sum of angles in a quadrilateral.
This problem involves a percentage reduction in price and a corresponding increase in quantity purchased for a fixed amount of money. We can set up equations based on the original and new prices and quantities to find the original price.
Let the original price of wheat be \(P\) per kg (in ₹).
The amount of wheat John could buy originally for ₹600 is \(\text{Quantity}_{\text{original}} = \frac{600}{P}\) kg.
The price of wheat is reduced by 25%. So, the new price \(P'\) is:
\[ P' = P - 0.25P = 0.75P \]With the new price, John can buy 5 kg more for ₹600. So, the new quantity is:
\[ \text{Quantity}_{\text{new}} = \frac{600}{0.75P} \]We are given that \(\text{Quantity}_{\text{new}} = \text{Quantity}_{\text{original}} + 5\). Substitute the expressions for quantities:
\[ \frac{600}{0.75P} = \frac{600}{P} + 5 \]To solve for \(P\), first simplify the equation:
\[ \frac{600}{0.75P} - \frac{600}{P} = 5 \]Factor out 600:
\[ 600 \left( \frac{1}{0.75P} - \frac{1}{P} \right) = 5 \]Find a common denominator inside the parenthesis:
\[ 600 \left( \frac{1}{0.75P} - \frac{0.75}{0.75P} \right) = 5 \]Simplify the term in the parenthesis:
\[ 600 \left( \frac{1 - 0.75}{0.75P} \right) = 5 \]Further simplification:
\[ 600 \left( \frac{0.25}{0.75P} \right) = 5 \]Note that \[\frac{0.25}{0.75} = \frac{1}{3}\]:
\[ 600 \left( \frac{1}{3P} \right) = 5 \]Solve for \(P\):
\[ \frac{600}{3P} = 5 \] \[ \frac{200}{P} = 5 \] \[ P = \frac{200}{5} \] \[ P = 40 \]The original price of wheat per kg is ₹40.
B) ₹40
The question asks to identify the region known as the "nursery of the Bengal army." This refers to a historical fact related to the recruitment practices of the British East India Company's army, particularly before the 1857 revolt.
A) Awadh — Awadh (Oudh) was indeed known as the "nursery of the Bengal army" because a significant number of its soldiers, particularly from the upper castes, were recruited from this region by the British East India Company.
The question asks about the source of litmus solution, which is a common natural indicator used to test for acids and bases. We need to identify the biological origin of this indicator.
Correct Option: C) Lichen is the correct answer because litmus solution is derived from lichens.
The question asks to identify the speaker of a specific statement regarding separate electorates during the Constituent Assembly debates on August 27, 1947. This requires knowledge of key figures and their positions on critical issues debated during the formation of the Indian Constitution.
A) Govind Ballabh Pant — Govind Ballabh Pant delivered a powerful speech in the Constituent Assembly on August 27, 1947, strongly opposing separate electorates. He argued that separate electorates would isolate minorities and prevent them from playing an effective role in the national political life, famously stating that they would be "suicidal to the minorities."
The question asks for the full form of the acronym COBOL. This is a common knowledge question related to computer programming languages. Recalling the exact meaning of each letter in the acronym is key to answering correctly.
Correct Option: D) Common Business Oriented Language
This option correctly spells out the full form of COBOL, which emphasizes its purpose as a language designed for business applications.
The question asks to identify the function key in Microsoft Excel that allows a user to switch into edit mode for a selected cell. Understanding the common shortcuts and functions of various function keys (F1-F12) in Excel is crucial for efficiency.
Correct Option: B) F2 is the function key used to switch a selected cell into edit mode in Excel.
The question states that a man purchased two articles at the same cost price but sold them at different profit percentages. We need to calculate the total cost price and total profit, then determine the overall profit percentage.
Identify the given information:
Calculate the total cost price:
Since both articles were purchased for ₹3,000 each:
\[ \text{Total CP}=3000+3000 \] \[ =6000 \]Therefore, the total cost price is ₹6,000.
Calculate the profit on the first article:
The first article was sold at a profit of 10%.
\[ \text{Profit}_1=\frac{10}{100}\times3000 \] \[ =300 \]Therefore, the profit on the first article is ₹300.
Calculate the profit on the second article:
The second article was sold at a profit of 5%.
\[ \text{Profit}_2=\frac{5}{100}\times3000 \] \[ =150 \]Therefore, the profit on the second article is ₹150.
Calculate the total profit:
\[ \text{Total Profit}=300+150 \] \[ =450 \]Therefore, the total profit earned is ₹450.
Calculate the overall profit percentage:
Using the formula:
\[ \text{Profit Percentage}= \frac{\text{Total Profit}}{\text{Total CP}}\times100 \]Substituting the values:
\[ =\frac{450}{6000}\times100 \] \[ =7.5\% \]Therefore, the overall profit percentage is 7.5%.
Correct Option: B) 7.5% — The man purchased two articles for ₹3,000 each, making the total cost price ₹6,000. He earned ₹300 profit on the first article and ₹150 profit on the second article. Therefore, the overall profit percentage is:
\[ \frac{300+150}{6000}\times100=7.5\% \]
Hence, Option B is the correct answer.
A) 15%: This is incorrect because adding the two profit percentages directly gives 15%, but the overall profit percentage must be calculated using the total profit and total cost price.
C) 8.5%: This is incorrect because the total profit of ₹450 on a total cost price of ₹6,000 gives 7.5%, not 8.5%.
D) 6.5%: This is incorrect because the calculated overall profit percentage is 7.5%, not 6.5%.
To find the area of a rhombus, we can use the formula involving its diagonals. We are given the side length and the length of one diagonal. We can use the property that the diagonals of a rhombus bisect each other at right angles to find the length of the other diagonal, and then calculate the area.
Let the side of the rhombus be \(a\). Given \(a = 10 \text{ cm}\).
Let the diagonals be \(d_1\) and \(d_2\). Given the longest diagonal \(d_1 = 16 \text{ cm}\).
The diagonals of a rhombus bisect each other at right angles. This means they divide the rhombus into four congruent right-angled triangles.
Consider one of these right-angled triangles. Its hypotenuse is the side of the rhombus (\(a\)), and its legs are half the lengths of the diagonals (\(\frac{d_1}{2}\) and \(\frac{d_2}{2}\)).
Half of the longest diagonal is \[\frac{d_1}{2} = \frac{16}{2} = 8 \text{ cm}\].
Using the Pythagorean theorem in one of the right-angled triangles:
\[ \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = a^2 \]Substitute the known values:
\[ (8)^2 + \left(\frac{d_2}{2}\right)^2 = (10)^2 \]\[ 64 + \left(\frac{d_2}{2}\right)^2 = 100 \]Solve for \(\left(\frac{d_2}{2}\right)^2\):
\[ \left(\frac{d_2}{2}\right)^2 = 100 - 64 \]\[ \left(\frac{d_2}{2}\right)^2 = 36 \]Take the square root to find \(\frac{d_2}{2}\):
\[ \frac{d_2}{2} = \sqrt{36} \]\[ \frac{d_2}{2} = 6 \text{ cm} \]Calculate the length of the second diagonal \(d_2\):
\[ d_2 = 2 \times 6 = 12 \text{ cm} \]The area of a rhombus is given by the formula:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]Substitute the values of \(d_1\) and \(d_2\):
\[ \text{Area} = \frac{1}{2} \times 16 \text{ cm} \times 12 \text{ cm} \]\[ \text{Area} = 8 \text{ cm} \times 12 \text{ cm} \]\[ \text{Area} = 96 \text{ cm}^2 \]Correct Option: C) 96 cm²