This problem can be solved using the rule of alligation, which is a method used to find the ratio in which two or more ingredients at given prices must be mixed to produce a mixture of a desired price. Alternatively, it can be solved using algebraic equations by setting up the total cost of the mixture.
Identify the given values:
Apply the Rule of Alligation:
The rule of alligation states that if two ingredients are mixed, the ratio of their quantities is inversely proportional to the difference between their individual prices and the mean price. We can represent this visually:
C2 (20) Cm (16.50) C1 (15)
\ /
\ /
\ /
(Cm - C1) : (C2 - Cm)
(16.50 - 15) : (20 - 16.50)
1.50 : 3.50
The ratio of the quantity of the first variety to the second variety is given by:
\[ \frac{\text{Quantity of 1st variety}}{\text{Quantity of 2nd variety}} = \frac{C_2 - C_m}{C_m - C_1} \]Calculate the differences:
Determine the ratio:
The required ratio of the first variety to the second variety is:
\[ \text{Ratio} = (C_2 - C_m) : (C_m - C_1) \]\[ \text{Ratio} = 3.50 : 1.50 \]Simplify the ratio:
To simplify, multiply both sides by 100 to remove decimals:
\[ 350 : 150 \]Divide both sides by their greatest common divisor, which is 50:
\[ \frac{350}{50} : \frac{150}{50} \]\[ 7 : 3 \]C) The ratio is 7 : 3. This matches our calculated ratio.
The area of the base of rectangular tank is 6500 cm2 and the volume of water contained in it is 2.6 cubic metres. The depth of water in the tank is:
To find the depth of water in the tank, we need to use the formula for the volume of a rectangular tank, which is given by \( \text{Volume} = \text{Area of base} \times \text{Depth} \). We are given the area of the base and the volume of water. The key is to ensure all units are consistent before performing calculations.
It's generally easier to work with meters. Let's convert the area of the base from \( \text{cm}^2 \) to \( \text{m}^2 \).
We know that \( 1 \text{ m} = 100 \text{ cm} \). Therefore, \( 1 \text{ m}^2 = (100 \text{ cm}) \times (100 \text{ cm}) = 10000 \text{ cm}^2 \).
So, the area of the base in \( \text{m}^2 \) is:
\[ A = 6500 \text{ cm}^2 \times \frac{1 \text{ m}^2}{10000 \text{ cm}^2} = 0.65 \text{ m}^2 \]The volume of water in a rectangular tank is given by:
\[ V = A \times D \]where \( D \) is the depth of the water.We need to find \( D \), so we can rearrange the formula:
\[ D = \frac{V}{A} \]Substitute the converted values into the formula:
\[ D = \frac{2.6 \text{ m}^3}{0.65 \text{ m}^2} \]\[ D = 4 \text{ m} \]B) 4 m is the correct depth of water in the tank after converting units and applying the volume formula.
The problem asks us to identify the 'odd man out' from a given series of numbers: 10, 14, 16, 18, 21, 24, 26. This typically involves finding a common property or pattern among most numbers and identifying the one that does not fit that pattern.
C) 21 — All the other numbers in the series (10, 14, 16, 18, 24, 26) are even numbers. 21 is the only odd number in the given set.
To find the odd man out in a series of numbers, we need to identify a common pattern or rule that applies to most of the numbers, and then find the number that does not follow this rule. We will examine properties like divisibility, sum of digits, or relationships between digits.
Correct Option: B) 427
These options follow the pattern of being divisible by 11, unlike 427.
The question asks to identify the sport traditionally regarded as the national sport of India. This requires knowledge of India's sporting history and cultural recognition.
Correct Option: C) Hockey is traditionally regarded as the national sport of India due to its unparalleled success on the international stage, particularly in the Olympic Games, during the early to mid-20th century. This historical dominance cemented its place in the national consciousness as India's premier sport.
The question asks for the city where Amer Fort is located. This is a factual question related to Indian geography and historical monuments. To answer correctly, one needs to recall the location of this famous fort.
Correct Option: B) Jaipur
The question asks to identify the historical figure known by the honorific title "Desh Bandhu". This requires knowledge of prominent personalities in Indian history, particularly during the freedom struggle, and their associated titles.
Correct Option: B) C.R. Das
The question asks for the city where Fatehpur Sikri is located. This is a factual question related to Indian history and geography, specifically about a prominent historical site built during the Mughal era.
Correct Option: C) Fatehpur Sikri is a historic city in the Agra district of Uttar Pradesh, India. It was founded in 1569 by the Mughal emperor Akbar and served as the capital of the Mughal Empire from 1571 to 1585. It is approximately 37 kilometers west of the city of Agra.
The question asks for the approximate breadth (gauge) of a railway broad gauge track. This is a factual question related to railway engineering standards, specifically the distance between the inner faces of the two rails.
C) 1.67 m — The standard broad gauge in India is \(1676 \text{ mm}\), which is approximately \(1.676 \text{ m}\). This rounds to \(1.67 \text{ m}\) and is the internationally recognized standard for broad gauge in many countries, including India.
The question asks about the number of stanzas in India's National Anthem. To answer this, one needs to recall the structure and composition of "Jana Gana Mana", which is the National Anthem of India.
D) The original full song "Bharoto Bhagyo Bidhata", from which the National Anthem is taken, comprises five stanzas. Therefore, our National Anthem, in its complete form, has five stanzas.