115% is equal to which of these fractions?
\( \frac{20}{3} \)
\( \frac{23}{20} \)
\( \frac{20}{23} \)
\( \frac{3}{20} \)
To convert a percentage to a fraction, we need to understand that "percent" means "per hundred". Therefore, a percentage value can be written as a fraction with a denominator of 100. After this conversion, the fraction should be simplified to its lowest terms.
Correct Option: B) \( \frac{23}{20} \)
We are given the ratio of the ages of Ajith and Ganesh seven years ago, and the product of their present ages. We need to find the ratio of their present ages. We will use variables to represent their ages, form an equation based on the given product, and solve for the unknown to find their present ages.
Let the ages of Ajith and Ganesh seven years ago be \(5x\) and \(7x\) respectively, based on the given ratio of \(5:7\).
Their present ages would then be:
We are given that the product of their present ages is 616. So, we can write the equation:
\[ (5x + 7)(7x + 7) = 616 \]Expand the equation:
\[ 35x^2 + 35x + 49x + 49 = 616 \]\[ 35x^2 + 84x + 49 = 616 \]Rearrange the equation into a standard quadratic form:
\[ 35x^2 + 84x + 49 - 616 = 0 \]\[ 35x^2 + 84x - 567 = 0 \]Divide the entire equation by the common factor 7 to simplify:
\[ 5x^2 + 12x - 81 = 0 \]Solve the quadratic equation for \(x\) using factorization or the quadratic formula. By factorization, we look for two numbers that multiply to \(5 \times (-81) = -405\) and add up to 12. These numbers are 27 and -15.
\[ 5x^2 + 27x - 15x - 81 = 0 \]\[ x(5x + 27) - 3(5x + 27) = 0 \]\[ (x - 3)(5x + 27) = 0 \]This gives two possible values for \(x\): \(x = 3\) or \(x = -\frac{27}{5}\). Since age cannot be negative, we take \(x = 3\).
Now, calculate their present ages using \(x = 3\):
Finally, find the ratio of their present ages:
\[ \text{Ratio} = \frac{22}{28} = \frac{11}{14} \]B) 11 : 14 is the correct ratio of their present ages.
The question asks to identify the hormone responsible for stimulating milk production after childbirth. This requires knowledge of the endocrine system and the specific roles of hormones involved in lactation.
Correct Option: A) Prolactin is the hormone primarily responsible for stimulating milk production (lactogenesis) in the mammary glands after childbirth. Its levels rise significantly during pregnancy and remain high after delivery, especially with suckling, to ensure continuous milk synthesis.
To identify the compound represented by the chemical formula K₂SO₄, we need to recognize the symbols for the elements and the polyatomic ion involved. K represents Potassium, and SO₄ represents the sulfate ion.
A) Potassium sulphate — The formula K₂SO₄ correctly represents Potassium sulfate. 'K' is Potassium and 'SO₄' is the sulfate ion.
To find the distance between the two buses, we need to calculate the effective distance covered by the first bus along the main road and then subtract the distance covered by the second bus from the total initial distance. The key is to understand that the first bus eventually returns to the main road, so we only need its displacement along the main road.
Correct Option: C) 65 km
The question asks about the color change of turmeric indicator in a basic solution. Turmeric is a natural indicator that changes color depending on whether it is in an acidic or basic medium. We need to recall the characteristic color changes of turmeric.
Correct Option: A) Yellow to red
To find the odd one out, we need to identify a common pattern or property among three of the given numbers and then find the number that does not follow this pattern. A common approach for such problems is to check if the numbers are cubes, squares, or related to them.
Correct Option: C) 125
The question asks to identify the Indian state for which Agartala is the capital. This is a direct knowledge-based question about Indian geography and administrative divisions.
Correct Option: C) Tripura. Agartala is the capital city of the Indian state of Tripura. It is the second-largest city in North-East India after Guwahati, both in municipal area and population.
The question asks to identify the hormone responsible for preventing blood glucose levels from dropping too low. This involves understanding the roles of various hormones in blood glucose regulation.
Correct Option: D) Glucagon — Glucagon is the hormone that counteracts low blood glucose levels by stimulating the liver to release stored glucose (glycogenolysis) and produce new glucose (gluconeogenesis), thereby raising blood glucose.