This problem involves work and time concepts. We can solve it by relating the efficiency of Anil and Balu to the amount of work they do per day. Since Anil is twice as efficient as Balu, we can express their individual work rates in terms of a common unit. Then, we use their combined work rate to find the total work and subsequently calculate the time Anil takes alone.
Define efficiencies: Let Balu's efficiency (work done per day) be \(B\). Since Anil is twice as efficient as Balu, Anil's efficiency will be \(A = 2B\).
Combined efficiency: When they work together, their combined efficiency is the sum of their individual efficiencies:
\[ \text{Combined Efficiency} = A + B = 2B + B = 3B \]Total work: They complete the task together in 12 days. The total work can be calculated as:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time Taken} \] \[ \text{Total Work} = 3B \times 12 = 36B \]Time taken by Anil alone: To find the time Anil takes to complete the task alone, we divide the total work by Anil's efficiency:
\[ \text{Time for Anil} = \frac{\text{Total Work}}{\text{Anil's Efficiency}} \] \[ \text{Time for Anil} = \frac{36B}{2B} = 18 \text{ days} \]Correct Option: B) 18
The question asks about the age eligibility criteria for the Pradhan Mantri Suraksha Bima Yojana (PMSBY) scheme. To answer this, one needs to recall the specific guidelines set for this government-backed insurance scheme.
B) 18 to 70 years — This is the correct age group for eligibility under the Pradhan Mantri Suraksha Bima Yojana (PMSBY).
The question asks to identify the Viceroy who announced the 'Dominion Status' offer in 1929. This requires knowledge of key historical events and the Viceroys associated with them during the British Raj in India.
C) Lord Irwin announced the 'Dominion Status' offer for India in 1929. This offer, known as the Irwin Declaration, was made on October 31, 1929, and aimed to appease Indian nationalist sentiments, though it was largely seen as insufficient and vague by Indian leaders.
To solve this problem, we first need to determine the Cost Price (CP) of the article using the given Selling Price (SP) and the percentage loss. Once the CP is known, we can calculate the new Selling Price required to achieve a 10% profit.
Therefore, the article should be sold for ₹220 to earn a 10% profit.
C) ₹220 — This is the correct price calculated to achieve a 10% profit after determining the cost price from the initial loss scenario.
To find the value of \(101^3\), we can use the algebraic identity for the cube of a binomial, \((a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). This method simplifies the calculation by breaking down \(101\) into \(100+1\).
Rewrite \(101\) as a sum of two numbers, one of which is a multiple of 10 or 100 for easier calculation. In this case, \(101 = 100 + 1\).
Apply the binomial expansion formula \((a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). Here, let \(a = 100\) and \(b = 1\).
Substitute the values of \(a\) and \(b\) into the formula:
\[ (100+1)^3 = (100)^3 + 3(100)^2(1) + 3(100)(1)^2 + (1)^3 \]Calculate each term:
Add these calculated terms together:
\[ 1,000,000 + 30,000 + 300 + 1 = 1,030,301 \]Correct Option: C) 1030301
The question asks to identify the main river to which the Mahananda river is a tributary. This requires knowledge of the major river systems in India, particularly the Ganga river system and its tributaries.
Correct Option: D) the Ganga river
The question asks us to identify the relationship between the first pair of words and apply the same relationship to the third word to find the fourth word. This is a common type of analogy question in competitive exams.
B) Student — A student is the individual who attends a college for the purpose of education, just as a patient attends a hospital for treatment.
The question asks to identify the organization responsible for creating, upgrading, maintaining, and managing civil aviation infrastructure in India, both on the ground and in the airspace, constituted in 1995. This requires knowledge of Indian aviation bodies and their historical formation.
Correct Option: B) Airport Authority of India
To find the HCF (Highest Common Factor) of a set of numbers, we need to find the largest number that divides all of them without leaving a remainder. We can do this by finding the prime factors of each number or by using the division method. In this case, since the numbers are relatively small, we can test divisibility by common prime factors or simply observe if any common factor greater than 1 exists.
C) 1 — As determined by checking divisibility and recognizing that 101 is a prime number, the only common factor among 81, 91, 101, and 111 is 1.
The smallest fraction that each of \( \frac{5}{14} \),\( \frac{6}{7} \)and \( \frac{10}{21} \) will divide exactly is:
\(\frac{60}{7}\)
\(\frac{30}{7}\)
\(\frac{30}{147}\)
\(\frac{50}{67}\)
To find the smallest fraction that each of the given fractions will divide exactly, we need to find the Least Common Multiple (LCM) of the given fractions. The formula for the LCM of fractions is:
\[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} \]We will apply this formula to the given fractions: \( \frac{5}{14} \), \( \frac{6}{7} \), and \( \frac{10}{21} \).
Identify the numerators and denominators:
Calculate the LCM of the numerators:
We need to find the LCM of \(5, 6, 10\).
To find the LCM, take the highest power of all prime factors involved:
\[ \text{LCM}(5, 6, 10) = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30 \]Calculate the HCF (GCD) of the denominators:
We need to find the HCF of \(14, 7, 21\).
To find the HCF, take the lowest power of common prime factors. The only common prime factor is \(7\).
\[ \text{HCF}(14, 7, 21) = 7^1 = 7 \]Apply the LCM of fractions formula:
\[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} = \frac{30}{7} \]B) \( \frac{30}{7} \) is the smallest fraction that each of the given fractions will divide exactly.