This is a logical reasoning question based on statements and conclusions. We need to evaluate each conclusion based on the information provided in the statements and determine which conclusions logically follow.
Let's analyze each statement and conclusion:
Statements:
Conclusions:
B) Only conclusion (iii) follows.
Two numbers are such that the sum of \( \frac{1}{3} \) of the first number and \( \frac{1}{2} \) of the second number is 8. The sum of \( \frac{1}{5} \) of the first number and \( \frac{1}{6} \) of the second number is 4. What is the largest of the two numbers?
This problem involves setting up a system of two linear equations with two variables based on the given information. We will then solve this system to find the values of the two numbers and identify the larger one.
Define variables: Let the first number be \(x\) and the second number be \(y\).
Formulate the first equation:
The sum of \( \frac{1}{3} \) of the first number and \( \frac{1}{2} \) of the second number is 8. This can be written as:
To eliminate fractions, multiply the entire equation by the least common multiple (LCM) of 3 and 2, which is 6:
\[ 6 \left( \frac{1}{3}x \right) + 6 \left( \frac{1}{2}y \right) = 6(8) \]\[ 2x + 3y = 48 \quad \text{(Equation 1)} \]Formulate the second equation:
The sum of \( \frac{1}{5} \) of the first number and \( \frac{1}{6} \) of the second number is 4. This can be written as:
To eliminate fractions, multiply the entire equation by the LCM of 5 and 6, which is 30:
\[ 30 \left( \frac{1}{5}x \right) + 30 \left( \frac{1}{6}y \right) = 30(4) \]\[ 6x + 5y = 120 \quad \text{(Equation 2)} \]Solve the system of equations:
We have the system:
Multiply Equation (1) by 3 to make the coefficients of \(x\) equal:
\[ 3(2x + 3y) = 3(48) \]\[ 6x + 9y = 144 \quad \text{(Equation 3)} \]Now, subtract Equation (2) from Equation (3):
\[ (6x + 9y) - (6x + 5y) = 144 - 120 \]\[ 6x + 9y - 6x - 5y = 24 \]\[ 4y = 24 \]\[ y = \frac{24}{4} \]\[ y = 6 \]Find the value of \(x\):
Substitute the value of \(y = 6\) into Equation (1):
Identify the largest number:
The two numbers are \(x = 15\) and \(y = 6\). The largest of these two numbers is 15.
Correct Option: D) 15
The two numbers are 15 and 6. The largest of these is 15.
This is a blood relation puzzle. We need to establish the relationships between the individuals mentioned and then deduce who Sandhya's daughter is. We will build a family tree step-by-step.
B) Jasmine — Based on the step-by-step deduction, Bruna's two great-granddaughters are Anum and Jasmine. Anum is Reena's granddaughter. Since Sandhya has only one daughter, and Bruna is Sandhya's maternal grandmother, Jasmine must be Sandhya's daughter to be Bruna's other great-granddaughter.
Study the given pattern carefully and select the number that can replace the question mark (?) in it.
The pattern involves two stars above two boxes. Each star contains a number, and each box contains a number. We need to identify the relationship between these numbers to find the missing number represented by a question mark.
Correct Option: A) 1
The question asks for the beginning year of the Swadeshi Movement. This requires knowledge of key events in modern Indian history, specifically the timeline of nationalist movements.
Correct Option: B) 1905. The Swadeshi Movement began in 1905 as a reaction to the Partition of Bengal by the British government. It was a powerful nationalist movement that emphasized self-reliance and the boycott of British goods.
The problem asks us to identify which courses of action logically follow from the given statement. The statement describes a plan to bake doughnuts for a guest tomorrow evening. We need to evaluate each course of action based on whether it is necessary or reasonable to achieve the stated goal.
Correct Option: D) Both (i) and (iii) follow.
This is a work and time problem. We will use the concept of work rate, where the rate is the reciprocal of the time taken to complete the work. We will set up equations based on the given information for the combined work rates of A, B, and C, and then solve for the individual work rate of C.
B) 48 hours
The question asks to identify the committee constituted for banking sector reforms in India. This requires knowledge of various committees formed by the Indian government for economic and financial reforms.
Correct Option: C) Narsimham Committee. The Narsimham Committee, chaired by M. Narasimham, was set up in 1991 (Narsimham Committee-I) and again in 1998 (Narsimham Committee-II) to suggest reforms for the financial and banking sectors in India. Its recommendations led to significant changes in the structure, regulation, and operations of Indian banks, aiming for greater efficiency and stability.
This problem involves finding the Least Common Multiple (LCM) of two numbers given their ratio and their Highest Common Factor (HCF). We will use the fundamental relationship between two numbers, their HCF, and their LCM.
Let the two numbers be \(A\) and \(B\). The ratio of the two numbers is given as 4 : 5. So, we can write:
\[ \frac{A}{B} = \frac{4}{5} \]Since the HCF of the two numbers is 3, we can express the numbers as multiples of their HCF. Let the common factor be \(x\). Then, the numbers can be written as \(4x\) and \(5x\).
However, the HCF is already given as 3. This means that the common factor \(x\) is 3. So, the numbers are:
\[ A = 4 \times \text{HCF} = 4 \times 3 = 12 \]\[ B = 5 \times \text{HCF} = 5 \times 3 = 15 \]Now we have the two numbers: 12 and 15.
We know the relationship between two numbers, their HCF, and their LCM:
\[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \]\[ A \times B = \text{HCF}(A, B) \times \text{LCM}(A, B) \]Substitute the values we have:
\[ 12 \times 15 = 3 \times \text{LCM} \]Calculate the product of the numbers:
\[ 12 \times 15 = 180 \]Now, solve for LCM:
\[ 180 = 3 \times \text{LCM} \]\[ \text{LCM} = \frac{180}{3} \]\[ \text{LCM} = 60 \]C) 60 is the correct LCM of the two numbers.
The question asks to identify the Indian athlete who became a Puma Brand ambassador in 2019. This requires knowledge of sports endorsements and current affairs related to Indian athletes.
Correct Option: A) Dutee Chand was appointed as a Puma Brand ambassador in 2019. She became the first Indian woman to sign an endorsement deal with the global sports brand.