To find the single equivalent discount for two successive discounts, we can assume an original price (e.g., 100 units) and apply each discount sequentially. Alternatively, we can use a direct formula for equivalent discount.
Alternative Method (Formula):
For two successive discounts of \(d_1\%\) and \(d_2\%\), the single equivalent discount \(D_{\text{eq}}\) is given by the formula:
Given \(d_1 = 30\%\) and \(d_2 = 35\%\):
\[ D_{\text{eq}} = \left(30 + 35 - \frac{30 \times 35}{100}\right)\% \]\[ D_{\text{eq}} = \left(65 - \frac{1050}{100}\right)\% \]\[ D_{\text{eq}} = (65 - 10.5)\% \]\[ D_{\text{eq}} = 54.5\% \]C) 54.5% is the single equivalent discount, as calculated by applying the discounts successively or using the equivalent discount formula.
The question asks for the biological process responsible for removing harmful metabolic wastes from the body. We need to identify the term that specifically describes this function.
Correct Option: D) excretion — Excretion is the biological process by which an organism eliminates metabolic waste products and other unwanted substances from its body. This includes the removal of urea, uric acid, creatinine, excess salts, and water through the kidneys, carbon dioxide through the lungs, and sweat through the skin.
The question asks about the primary state where the Jivitputrika festival is celebrated, especially in the context of recent news. This requires knowledge of Indian festivals and their geographical distribution.
Correct Option: C) Bihar is the primary state where the Jivitputrika festival is celebrated with great devotion, especially by mothers fasting for the longevity and prosperity of their children. It is also observed in parts of Jharkhand and Uttar Pradesh, and in Nepal.
The problem presents a series of letter groups, and we need to find the next group in the sequence. We will analyze the pattern for each letter's position (first, second, and third) across the given groups based on the English alphabetical order.
The pattern for the first letter is a decrease of 2 positions in the alphabet (Z \(-2\) = X, X \(-2\) = V, V \(-2\) = T). Following this pattern, the next first letter should be T \(-2\) = R (18th letter).
The pattern for the second letter is also a decrease of 2 positions in the alphabet (T \(-2\) = R, R \(-2\) = P, P \(-2\) = N). Following this pattern, the next second letter should be N \(-2\) = L (12th letter).
The pattern for the third letter is also a decrease of 2 positions in the alphabet (Q \(-2\) = O, O \(-2\) = M, M \(-2\) = K). Following this pattern, the next third letter should be K \(-2\) = I (9th letter).
The next group in the series will be formed by combining the next first, second, and third letters: R, L, I. So, the group is RLI.
Correct Option: C) RLI
The problem asks us to calculate the total amount Aruna has to pay after 2 years on a compound interest loan. We are given the principal amount, the annual interest rate, and the duration. We will use the compound interest formula to find the total amount.
The formula for the amount (\(A\)) after \(T\) years when interest is compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]The total amount paid by Aruna after 2 years is ₹10,890.
Correct Option: B) ₹10,890
The problem asks us to find the values of X and Y that maintain a consistent mathematical pattern between two number pairs. We need to identify the operation that transforms the first number into the second number in the given pair, and then apply that same operation to find X and Y.
Analyze the given information: The pattern is X : 529 :: 21 : Y. This means the relationship between X and 529 is the same as the relationship between 21 and Y.
Observe the number 529. It is a perfect square. Let's find its square root:
\[ \sqrt{529} = 23 \]This suggests that the second number in the pair might be the square of some number related to the first number. If 529 is the square of 23, then the first number (X) must be related to 23.
Consider the relationship: If the second number is the square of (first number + k), where k is a constant, then for the first pair (X : 529), we have:
\[ (X + k)^2 = 529 \]\[ X + k = 23 \quad \text{(since X and k are positive integers)} \]Now, let's test the options for X. We are looking for an X such that \(X+k=23\) for some constant \(k\). And then, for the second pair (21 : Y), the same constant \(k\) should apply, so that \((21+k)^2 = Y\).
Let's check option D, where X = 18.
The pattern is: The second number is the square of (the first number + 5).
If X = 18, then the pattern is \( (18 + 5)^2 = 23^2 = 529 \). Applying the same pattern to the second pair, if the first number is 21, then \( Y = (21 + 5)^2 = 26^2 = 676 \). Therefore, X = 18 and Y = 676 fit the pattern.
This problem involves trigonometry, specifically the concept of angles of depression. We need to find the horizontal distances from the base of the tower to each road using the given height of the tower and the angles of depression. Since the roads are on opposite sides of the tower, the total distance between them will be the sum of these two horizontal distances.
Let the height of the tower be \(h = 10 \text{ m}\).
Let the top of the tower be point A, and its base be point B. Let the two roads be at points C and D on the ground, such that B lies between C and D.
The angles of depression from the top of the tower (A) to the roads (C and D) are 30° and 45° respectively. Due to alternate interior angles, the angles of elevation from the roads to the top of the tower are also 30° and 45°.
Consider the right-angled triangle ABC, where \(\angle ACB = 30^\circ\).
\[ \tan(30^\circ) = \frac{\text{AB}}{\text{BC}} \]\[ \frac{1}{\sqrt{3}} = \frac{10}{\text{BC}} \]\[ \text{BC} = 10\sqrt{3} \text{ m} \]Consider the right-angled triangle ABD, where \(\angle ADB = 45^\circ\).
\[ \tan(45^\circ) = \frac{\text{AB}}{\text{BD}} \]\[ 1 = \frac{10}{\text{BD}} \]\[ \text{BD} = 10 \text{ m} \]The total distance between the roads is the sum of BC and BD.
\[ \text{Distance} = \text{BC} + \text{BD} \]\[ \text{Distance} = 10\sqrt{3} + 10 \]\[ \text{Distance} = 10(\sqrt{3} + 1) \]Substitute the approximate value of \(\sqrt{3} \approx 1.732\).
\[ \text{Distance} = 10(1.732 + 1) \]\[ \text{Distance} = 10(2.732) \]\[ \text{Distance} = 27.32 \text{ m} \]B) The calculated distance between the roads is approximately \(27.32 \text{ m}\), which matches option B.
To find the total count of prime numbers less than 50, we need to list all prime numbers starting from 2 and ending before 50. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
There are 15 prime numbers in the list.
Correct Option: B) 15
This problem involves determining relative positions of towns based on given directional clues. We can solve this by drawing a rough diagram or visualizing the positions on a compass.
Correct Option: D) Southeast. Based on the consolidated information, Town E lies to the southeast of Town C.
To solve this letter series, we need to identify the pattern in the progression of each letter's position within the English alphabet. We will analyze the first, second, and third letters of each term separately.
Analyze the first letter of each term:
The pattern for the first letter is an increment of 2 (C + 2 = E, E + 2 = G, G + 2 = I). Following this pattern, the next first letter will be I + 2 = K (11th letter).
Analyze the second letter of each term:
The pattern for the second letter is also an increment of 2 (G + 2 = I, I + 2 = K, K + 2 = M). Following this pattern, the next second letter will be M + 2 = O (15th letter).
Analyze the third letter of each term:
The pattern for the third letter is also an increment of 2 (M + 2 = O, O + 2 = Q, Q + 2 = S). Following this pattern, the next third letter will be S + 2 = U (21st letter).
Combine the next letters:
The next term in the series will be formed by combining the next first, second, and third letters: K, O, U.
Correct Option: D) KOU