The question asks about a specific partnership between WHO and the Food and Beverage Alliance aimed at eliminating a particular substance from the global food supply by 2023. This requires knowledge of public health initiatives related to food safety and nutrition.
Correct Option: B) Trans fat
The World Health Organization (WHO) has indeed partnered with the Food and Beverage Alliance to achieve its target of eliminating industrially produced trans fat from the global food supply by 2023. This initiative is part of WHO's broader efforts to reduce non-communicable diseases, particularly cardiovascular diseases, which are strongly linked to trans fat consumption. Industrially produced trans fats are found in hardened vegetable oils, often used in baked goods, fried foods, and processed snacks, and have no known health benefits.
This problem involves the relationship between the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD) of two numbers. A fundamental property states that for any two positive integers, the product of the numbers is equal to the product of their LCM and GCD.
Correct Option: A) 39
To find the ratio of the speeds, we need to express the speed of the cyclist and the speed of the jogger in terms of distance and time. The fundamental formula for speed is \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\).
Let the distance covered by the cyclist be \(d\).
Let the time taken by the cyclist be \(t\).
The speed of the cyclist (\(S_c\)) is given by:
\[ S_c = \frac{d}{t} \]The jogger covers half the distance, so the distance covered by the jogger (\(d_j\)) is \(\frac{d}{2}\).
The jogger takes double the time, so the time taken by the jogger (\(t_j\)) is \(2t\).
The speed of the jogger (\(S_j\)) is given by:
\[ S_j = \frac{d_j}{t_j} = \frac{\frac{d}{2}}{2t} \]Simplify the expression for \(S_j\):
\[ S_j = \frac{d}{2 \times 2t} = \frac{d}{4t} \]We need to find the ratio of the speed of the cyclist to the speed of the jogger, which is \(\frac{S_c}{S_j}\).
\[ \frac{S_c}{S_j} = \frac{\frac{d}{t}}{\frac{d}{4t}} \]To simplify this complex fraction, multiply the numerator by the reciprocal of the denominator:
\[ \frac{S_c}{S_j} = \frac{d}{t} \times \frac{4t}{d} \]Cancel out \(d\) and \(t\):
\[ \frac{S_c}{S_j} = 4 \]So, the ratio is \(4:1\).
B) The ratio of the speed of the cyclist to the speed of the jogger is \(4:1\).
The problem asks us to find the area of a sector given the radius and a relationship between the arc length and the radius. We will use the formulas for the arc length of a sector and the area of a sector.
B) \(486 \text{ cm}^2\)
The calculation shows that the area of the sector is \(486 \text{ cm}^2\).
To find the ratio in which Mahesh and Hareesh divide the profits, we need to calculate the equivalent investment for each person over the entire duration of the business. Profit is distributed in proportion to the product of the investment amount and the time for which it was invested.
Mahesh invested ₹20,000 for the entire duration of the business. Since the problem doesn't specify the total duration, we assume it's for a standard period, say 12 months, or simply consider the relative time units. For simplicity in ratio calculation, we can consider the time unit as 'months'.
Mahesh's investment equivalent \( = \text{Investment} \times \text{Time} \)
\[ \text{Mahesh's investment equivalent} = \text{₹}20,000 \times 12 \text{ months} = \text{₹}240,000 \]Hareesh initially invested ₹30,000 for 3 months. After 3 months, he withdrew ₹5,000, so his remaining investment was \(\text{₹}30,000 - \text{₹}5,000 = \text{₹}25,000\). This remaining amount was invested for the rest of the year, i.e., \(12 - 3 = 9\) months.
Hareesh's investment equivalent \( = (\text{Initial Investment} \times \text{Time}_1) + (\text{Remaining Investment} \times \text{Time}_2) \)
\[ \text{Hareesh's investment equivalent} = (\text{₹}30,000 \times 3 \text{ months}) + (\text{₹}25,000 \times 9 \text{ months}) \] \[ = \text{₹}90,000 + \text{₹}225,000 \] \[ = \text{₹}315,000 \]The ratio of their profits will be the ratio of their investment equivalents.
\[ \text{Ratio (Mahesh : Hareesh)} = \text{Mahesh's investment equivalent} : \text{Hareesh's investment equivalent} \] \[ = \text{₹}240,000 : \text{₹}315,000 \]To simplify the ratio, divide both sides by 1,000:
\[ = 240 : 315 \]Now, divide both sides by their greatest common divisor. Both numbers are divisible by 5:
\[ = \frac{240}{5} : \frac{315}{5} \] \[ = 48 : 63 \]Both numbers are divisible by 3:
\[ = \frac{48}{3} : \frac{63}{3} \] \[ = 16 : 21 \]D) The calculated ratio of profits is 16 : 21.
This problem involves calculating the combined work rate of two individuals to find the total time taken to complete a task together. We will use the concept of work done per day (rate) and then sum their individual rates to find the combined rate. The reciprocal of the combined rate will give the total time.
Calculate Rama's daily work rate:
If Rama can complete a task in 20 days, then in one day, Rama completes \(\frac{1}{20}\) of the task.
\[ \text{Rama's daily work} = \frac{1}{20} \text{ task/day} \]Calculate Krishna's daily work rate:
If Krishna can complete the same task in 30 days, then in one day, Krishna completes \(\frac{1}{30}\) of the task.
\[ \text{Krishna's daily work} = \frac{1}{30} \text{ task/day} \]Calculate their combined daily work rate:
When working together, their daily work rates add up.
\[ \text{Combined daily work} = \text{Rama's daily work} + \text{Krishna's daily work} \] \[ \text{Combined daily work} = \frac{1}{20} + \frac{1}{30} \]To add these fractions, find a common denominator, which is 60.
\[ \text{Combined daily work} = \frac{3}{60} + \frac{2}{60} \] \[ \text{Combined daily work} = \frac{3+2}{60} = \frac{5}{60} \] \[ \text{Combined daily work} = \frac{1}{12} \text{ task/day} \]Calculate the total time taken to complete the task together:
If they complete \(\frac{1}{12}\) of the task in one day, then they will complete the entire task (1 whole task) in the reciprocal of this rate.
\[ \text{Time taken} = \frac{1}{\text{Combined daily work}} \] \[ \text{Time taken} = \frac{1}{\frac{1}{12}} = 12 \text{ days} \]Correct Option: A) 12 days
The question asks to identify the ruler who established Sera-i-Adl, a specific market in Delhi for manufactured and exported goods with administratively fixed prices. This points to a significant economic reform during the Delhi Sultanate period, particularly related to market control and price regulation. We need to recall the economic policies of the prominent rulers mentioned in the options.
Alauddin Khalji (1296-1316 AD) was renowned for his comprehensive market control policies aimed at maintaining a large army at a low cost and preventing hoarding. He established several markets, each specializing in different commodities. Sera-i-Adl was one such market, specifically designated for manufactured goods, imported items, and expensive commodities. Prices in this market, like others under his system, were strictly fixed by the administration.
C) Alauddin Khalji established Sera-i-Adl as part of his extensive market control measures. This market dealt with manufactured goods, imported items, and expensive commodities, with prices fixed by the state. His objective was to ensure the availability of goods at reasonable prices for his soldiers and the general populace, thereby stabilizing the economy and preventing inflation.
This problem involves work and time. We need to find the individual time taken by B to complete a job, given the relative efficiency of A and B, and their combined time to finish the job. We can solve this by relating their work rates.
Define work rates: Let the amount of work B does in one day be \(x\) units. This is B's work rate.
Determine A's work rate: The problem states that A works twice as fast as B. Therefore, A's work rate is \(2x\) units per day.
Calculate combined work rate: When A and B work together, their combined work rate is the sum of their individual work rates:
\[ \text{Combined work rate} = \text{A's rate} + \text{B's rate} = 2x + x = 3x \text{ units per day} \]Use combined time to find total work: They finish the job together in 12 days. If they complete \(3x\) units of work per day, the total work for the entire job is:
\[ \text{Total work} = \text{Combined work rate} \times \text{Time taken} = 3x \times 12 = 36x \text{ units} \]Calculate time for B alone: To find how many days B will take to finish the job alone, we divide the total work by B's individual work rate:
\[ \text{Time for B alone} = \frac{\text{Total work}}{\text{B's work rate}} = \frac{36x}{x} = 36 \text{ days} \]B) 36 days. This is derived from calculating the total work based on their combined efficiency and then dividing it by B's individual efficiency.
The question asks for the main feature of mixed farming. We need to understand the definition of mixed farming and differentiate it from other agricultural practices.
Correct Option: D) Rearing of animals and cultivation of crops together
The question asks to identify the type of economic system that best describes the Indian economy. Understanding the characteristics of different economic systems is crucial to answering this question.
Correct Option: B) mixed economy
India's economy is characterized by the coexistence of both the private and public sectors. The government plays a significant role in economic planning, regulation, and the provision of public goods and services, while the private sector drives innovation, production, and consumption in many areas. This blend of market forces and government intervention is the hallmark of a mixed economy.