The problem states a relationship between a number, its 60%, and the constant 120. We need to first find the number and then calculate 60% of that number. We can set up an algebraic equation to represent the given information and solve for the unknown number.
C) 180 is the correct answer. This is 60% of the number 300, which satisfies the initial condition.
The problem provides a ratio between two variables, \(x\) and \(y\), and asks for the ratio of their sum to their difference. We can express \(x\) and \(y\) in terms of a common multiple based on the given ratio and then substitute these expressions into the required ratio.
We are given that \(x : y = 8 : 3\).
This can be written as a fraction:
\[ \frac{x}{y} = \frac{8}{3} \]From the ratio, we can assume that \(x\) and \(y\) are multiples of 8 and 3, respectively, with the same constant of proportionality. Let this constant be \(k\).
\[ x = 8k \]\[ y = 3k \]Substitute the expressions for \(x\) and \(y\):
\[ x + y = 8k + 3k = 11k \]Substitute the expressions for \(x\) and \(y\):
\[ x - y = 8k - 3k = 5k \]Now, form the ratio of the sum to the difference:
\[ (x + y) : (x - y) = 11k : 5k \]Since \(k\) is a common factor and \(k \neq 0\) (as \(x\) and \(y\) are not zero), we can cancel \(k\):
\[ 11k : 5k = 11 : 5 \]B) The ratio \((x + y) : (x - y)\) is \(11 : 5\).
Triangle ABC is similar to triangle DEF with \(\frac{\overline{BC}}{\overline{EF}}\)= \( \frac{1}{4} \). Find \(\frac{\operatorname{Area}(\triangle DEF)}{\operatorname{Area}(\triangle ABC)}\).
The problem involves two similar triangles, \(\triangle ABC\) and \(\triangle DEF\), and asks for the ratio of their areas given the ratio of their corresponding sides. The key concept here is the property of similar triangles which states that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
B) 16
This problem involves work and time, where the efficiency of men and women can be compared. We will first determine the individual work rate of one man and one woman, then find the combined work rate of 4 men and 6 women, and finally calculate the time required to complete the work.
Let the total work be \(W\). The work done by 48 men in 5 days is \(W\). The work done by 40 women in 9 days is also \(W\).
From the first statement:
\[ 48 \text{ men} \times 5 \text{ days} = W \]\[ 1 \text{ man's 1-day work} = \frac{W}{48 \times 5} = \frac{W}{240} \]\[ 1 \text{ man's 1-day work} = \frac{1}{240} \text{ of the total work} \]From the second statement:
\[ 40 \text{ women} \times 9 \text{ days} = W \]\[ 1 \text{ woman's 1-day work} = \frac{W}{40 \times 9} = \frac{W}{360} \]\[ 1 \text{ woman's 1-day work} = \frac{1}{360} \text{ of the total work} \]4 men's 1-day work:
\[ 4 \times \frac{1}{240} = \frac{4}{240} = \frac{1}{60} \text{ of the total work} \]6 women's 1-day work:
\[ 6 \times \frac{1}{360} = \frac{6}{360} = \frac{1}{60} \text{ of the total work} \]Combined 1-day work of 4 men and 6 women:
\[ \frac{1}{60} + \frac{1}{60} = \frac{2}{60} = \frac{1}{30} \text{ of the total work} \]If 4 men and 6 women together complete \(\frac{1}{30}\) of the work in 1 day, then they will complete the entire work in:
\[ \text{Days} = \frac{\text{Total Work}}{\text{Combined 1-day work}} = \frac{1}{\frac{1}{30}} = 30 \text{ days} \]Correct Option: B) 30 days
The question asks to identify the correct statement about a magnetic field. We need to evaluate each option based on the fundamental properties of magnetic fields.
Correct Option: A) Its direction at any point is measured by a magnetic compass.
This question tests the fundamental definitions of basic kinematic quantities: displacement, distance, velocity, and speed. We need to identify which of these terms precisely describes the total length of the path traversed by a moving object.
Correct Option: B) Distance is defined as the total path length covered by a moving body. It is a scalar quantity, meaning it only has magnitude and no direction.
We need to calculate the percentage increase in expenditure. We can assume an initial monthly income to simplify calculations. Then, we will calculate the initial savings and expenditure. Next, we will calculate the new income, new savings, and new expenditure based on the given percentage increases. Finally, we will find the percentage increase in expenditure.
C) 20%
To solve this number series problem, we need to identify the pattern or rule that governs the sequence of numbers. We will look for differences between consecutive terms or other mathematical relationships.
The differences between consecutive terms are \(9, 11, 13, 15\). This is an arithmetic progression where each subsequent difference increases by 2. These are consecutive odd numbers starting from 9.
Following the pattern, the next difference should be \(15 + 2 = 17\).
To find the next term after 72, we add the predicted difference to 72:
\[ 72 + 17 = 89 \]A) 89 is the correct option because it follows the established pattern where the difference between consecutive terms increases by 2 (9, 11, 13, 15, 17).
To solve this problem, we need to track Q's movement step-by-step, noting the distance and direction for each segment. We can visualize this as movement on a 2D coordinate plane or simply keep track of net displacement in North-South and East-West directions. The final position relative to the starting point A will tell us the shortest distance and direction needed to return to A.
D) 3 km towards the West. To return to Point A from Point P (which is 3 km East of A), Q must drive 3 km towards the West.
This is a coding-decoding question where we need to identify the pattern in the given pairs of alphanumeric codes. The pattern usually involves operations on the alphabetical positions and the numerical parts of the codes.
D) EI29 is the correct option as it follows the established pattern: subtract 11 from the alphabetical positions (wrapping around if negative) and add 7 to the numerical part.