This problem involves work and wages. The wages are distributed in proportion to the amount of work done by each individual. We need to calculate the individual work rates, then determine the fraction of work done by each person, and finally, calculate their share of the total amount.
A alone can do the work in 6 days. So, A's one day's work is:
\[ \text{A's 1 day's work} = \frac{1}{6} \]B alone can do the work in 8 days. So, B's one day's work is:
\[ \text{B's 1 day's work} = \frac{1}{8} \]With the help of C, they can finish the work in 3 days. So, (A + B + C)'s one day's work is:
\[ \text{(A + B + C)'s 1 day's work} = \frac{1}{3} \]C's one day's work can be found by subtracting A's and B's one day's work from (A + B + C)'s one day's work:
\[ \text{C's 1 day's work} = \text{(A + B + C)'s 1 day's work} - \text{A's 1 day's work} - \text{B's 1 day's work} \]\[ \text{C's 1 day's work} = \frac{1}{3} - \frac{1}{6} - \frac{1}{8} \]\[ \text{C's 1 day's work} = \frac{8 - 4 - 3}{24} = \frac{1}{24} \]Since they all work for 3 days to complete the work, the ratio of their work done is proportional to their one day's work:
\[ \text{Ratio of work done by A : B : C} = \text{A's 1 day's work} : \text{B's 1 day's work} : \text{C's 1 day's work} \]\[ \text{Ratio} = \frac{1}{6} : \frac{1}{8} : \frac{1}{24} \]To simplify the ratio, multiply by the LCM of 6, 8, and 24, which is 24:\[ \text{Ratio} = \left(\frac{1}{6} \times 24\right) : \left(\frac{1}{8} \times 24\right) : \left(\frac{1}{24} \times 24\right) \]\[ \text{Ratio} = 4 : 3 : 1 \]The total amount for the work is Rs 800. A's share will be based on the ratio of work done by A to the total ratio:
\[ \text{A's share} = \frac{\text{A's ratio}}{\text{Sum of ratios}} \times \text{Total amount} \]\[ \text{A's share} = \frac{4}{4 + 3 + 1} \times 800 \]\[ \text{A's share} = \frac{4}{8} \times 800 \]\[ \text{A's share} = \frac{1}{2} \times 800 = 400 \]C) 400
The question asks about the normal pH range within which the human body functions. This is a fundamental concept in biology and chemistry, specifically related to homeostasis. We need to recall the typical pH of human blood and other bodily fluids.
B) 7 to 7.8 — This range accurately represents the slightly alkaline conditions required for most bodily functions. The pH of human blood is tightly regulated between 7.35 and 7.45. The option 7 to 7.8 covers this critical physiological range.
The question asks to identify the state that is NOT part of the Indian Himalayan region. This requires knowledge of the geographical location of Indian states relative to the Himalayan mountain range.
D) Bihar is predominantly a plain state in the Gangetic plain and is not considered part of the Indian Himalayan region.
This problem involves calculating temperatures using given average temperatures over different periods. We will use the formula for average: Average = Sum of values / Number of values. By setting up equations based on the given averages, we can find the sum of temperatures for specific days and then isolate the unknown temperature.
Let \(T_M\), \(T_{Tu}\), \(T_W\), and \(T_S\) represent the temperatures on Monday, Tuesday, Wednesday, and Sunday, respectively.
From the first statement, "The average temperature on Monday, Tuesday and Wednesday was 32°C":
\[ \frac{T_M + T_{Tu} + T_W}{3} = 32^\circ\text{C} \]Calculate the sum of temperatures for Monday, Tuesday, and Wednesday:
\[ T_M + T_{Tu} + T_W = 32 \times 3 = 96^\circ\text{C} \quad \text{(Equation 1)} \]From the second statement, "the average temperature on Sunday, Monday and Tuesday was 36°C":
\[ \frac{T_S + T_M + T_{Tu}}{3} = 36^\circ\text{C} \]Calculate the sum of temperatures for Sunday, Monday, and Tuesday:
\[ T_S + T_M + T_{Tu} = 36 \times 3 = 108^\circ\text{C} \quad \text{(Equation 2)} \]We are given that the temperature on Sunday was 39°C, so \(T_S = 39^\circ\text{C}\).
Substitute the value of \(T_S\) into Equation 2:
\[ 39 + T_M + T_{Tu} = 108^\circ\text{C} \]From this, we can find the sum of temperatures for Monday and Tuesday:
\[ T_M + T_{Tu} = 108 - 39 = 69^\circ\text{C} \quad \text{(Equation 3)} \]Now, substitute Equation 3 into Equation 1:
\[ (T_M + T_{Tu}) + T_W = 96^\circ\text{C} \]\[ 69 + T_W = 96^\circ\text{C} \]Solve for \(T_W\):
\[ T_W = 96 - 69 = 27^\circ\text{C} \]Therefore, the temperature on Wednesday was 27°C.
B) 27°C — The calculation shows that the temperature on Wednesday is 27°C.
This question tests the basic understanding of carbon's valency and its ability to form stable compounds with hydrogen. Carbon typically forms four bonds. We need to check if the given chemical formulas adhere to this fundamental rule of valency.
Correct Option: C) CH₆ — This compound cannot exist because carbon's valency is 4, meaning it can form a maximum of four bonds. In CH₆, carbon would need to form six bonds, which is chemically impossible for carbon.
The problem asks us to find a number that completes an analogy. We need to identify the relationship between the first and second numbers, and the third and fourth numbers, and then apply the same relationship to the fifth number to find the sixth number.
B) 170 is the correct answer because it follows the pattern \(N^2 + 1\) established by the previous pairs.
To determine the true statement, we need to evaluate each option based on the definitions and properties of prime numbers.
Correct Option: B) All prime numbers except the number 2 are odd numbers.
Explanation: A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. The number 2 is prime because its only divisors are 1 and 2. It is also an even number. Any other even number (e.g., 4, 6, 8, ...) is divisible by 1, by itself, and by 2, meaning it has at least three divisors, and thus cannot be prime. Therefore, 2 is the only even prime number, and all other prime numbers must be odd.
The question describes a common medical application where a substance is mixed with water to support fractured bones. This substance needs to harden quickly to provide stability. We need to identify the chemical compound commonly used for this purpose.
C) Plaster of Paris is calcium sulfate hemihydrate \[\(\text{CaSO}_4 \cdot \frac{1}{2}\text{H}_2\text{O}\]\). It is widely used in hospitals for setting fractured bones. When mixed with water, it forms a paste that quickly hardens into gypsum, providing rigid support to the fractured bone.
We need to find Kamal's present age. We are given relationships between the present ages of Kamal, Vishnu, and Deeksha, and the sum of their ages three years ago. We will set up equations based on these relationships and solve for the unknown ages.
Define variables for present ages:
Formulate equations based on present age relationships:
Determine ages 3 years ago:
Formulate equation based on the sum of ages 3 years ago:
Substitute Equations 1 and 2 into Equation 3:
Substitute \(K = 3V\) and \(D = V - 3\) into \(K + V + D = 72\):
\[ (3V) + V + (V - 3) = 72 \]Solve for Vishnu's present age (\(V\)):
\[ 5V - 3 = 72 \] \[ 5V = 72 + 3 \] \[ 5V = 75 \] \[ V = \frac{75}{5} \] \[ V = 15 \text{ years} \]Calculate Kamal's present age (\(K\)):
Using Equation 1, \(K = 3V\):
\[ K = 3 \times 15 \] \[ K = 45 \text{ years} \]Correct Option: B) 45
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This stands for Brackets/Parentheses, Orders/Exponents, Division/Multiplication (from left to right), and Addition/Subtraction (from left to right).
Thus, the value of the expression is 55.
Correct Option: C) 55