A man sold an article for ₹360 by first giving a d% discount on its marked price, and then another discount having the same nominal value (in ₹). If the marked price of the article is ₹2,250, then what is the value of d?
The problem involves calculating a discount percentage given two successive discounts. The first discount is a percentage 'd' on the marked price, and the second discount is a fixed amount (nominal value) that is equal to the value of the first discount. We need to find the value of 'd'.
Let the Marked Price (MP) be ₹2,250.
The first discount is d% on the Marked Price.
\[ \text{First Discount Amount} = \frac{d}{100} \times \text{MP} = \frac{d}{100} \times 2250 = 22.5d \]Price after the first discount:
\[ \text{Price}_1 = \text{MP} - \text{First Discount Amount} = 2250 - 22.5d \]The second discount has the same nominal value (in ₹) as the first discount. So, the Second Discount Amount is also \(22.5d\).
The final Selling Price (SP) is ₹360.
The Selling Price is obtained by subtracting the second discount from the price after the first discount:
\[ \text{SP} = \text{Price}_1 - \text{Second Discount Amount} \] \[ 360 = (2250 - 22.5d) - 22.5d \]Now, solve the equation for d:
\[ 360 = 2250 - 45d \] \[ 45d = 2250 - 360 \] \[ 45d = 1890 \] \[ d = \frac{1890}{45} \] \[ d = 42 \]C) 42 is the correct value for d, as calculated from the given conditions.
The problem asks us to find the missing letter-clusters, # and %, based on the pattern and relationship observed in an analogy. We need to determine the rule applied to transform the first letter-cluster into the second in the given pair, and then apply the same rule to find the missing clusters.
D) # = PJF, % = MGC
To find the mode of a given set of data, we need to identify the value that appears most frequently in the dataset. The mode is a measure of central tendency.
Correct Option: B) 18 is the mode because it appears 3 times, which is more than any other mark in the given data set.
The question asks about Fleming's Right-Hand Rule, which is used to determine the direction of induced current when a conductor moves in a magnetic field. We need to recall what each finger (thumb, forefinger, middle finger) represents in this rule.
A) Direction of motion — In Fleming's Right-Hand Rule, the thumb represents the direction of the motion or thrust of the conductor.
The problem asks us to find a relationship between pairs of numbers. We are given two examples: 119 is related to 205, and 145 is related to 231. We need to identify the logical rule governing this relationship and then apply it to find the number related to 132.
Let's find the difference between the two numbers:
\[ 205 - 119 = 86 \]Let's find the difference between these two numbers:
\[ 231 - 145 = 86 \]In both given examples, the second number is obtained by adding 86 to the first number. This suggests a consistent pattern where the relationship is simply adding 86 to the given number.
Following the identified logic, to find the number related to 132, we need to add 86 to 132:
\[ 132 + 86 = 218 \]The calculated number is 218, which matches option D.
D) 218 is the correct answer because, following the pattern of adding 86 to the first number, \(132 + 86 = 218\).
This problem involves calculating the combined work rate of two individuals, A and B, to find the total time taken to complete a task when working together. We will use the concept of work and time, where the work done per day is the reciprocal of the total days taken to complete the work.
A) 1.9 is the correct answer, as calculated above.
This problem involves decoding a relationship expression based on given symbolic representations. We need to break down the expression 'S + D × F ÷ G − H' step-by-step, interpreting each symbol to build a family tree or relationship diagram, and then determine the relationship between S and H.
Since 'A + B' means 'A is the son of B', 'S + D' means 'S is the son of D'.
Since 'A × B' means 'A is the wife of B', 'D × F' means 'D is the wife of F'.
Since 'A ÷ B' means 'A is the father of B', 'F ÷ G' means 'F is the father of G'.
Since 'A − B' means 'A is the brother of B', 'G − H' means 'G is the brother of H'.
From the above steps, S, G, and H are all children of F and D. We know S is male (son of D). G is male (brother of H). H's gender is not specified, but H is a sibling of S. Therefore, S is the brother of H.
Correct Option: A) Brother
To find the average speed, we need to calculate the total distance traveled and the total time taken. The average speed is the total distance divided by the total time. Since the distance covered while going from A to B is the same as returning from B to A, we can use the formula for average speed when the distance is constant.
Namit travels from A to B and then returns from B to A. So, the total distance is twice the distance between A and B.
\[ \text{Total Distance} = D + D = 2D = 2 \times 530 \text{ km} = 1060 \text{ km} \]Time = Distance / Speed
Average Speed = Total Distance / Total Time
\[ \text{Average Speed} = \frac{2D}{T_1 + T_2} = \frac{2 \times 530}{530 \left( \frac{114}{2849} \right)} \] \[ \text{Average Speed} = \frac{2}{\frac{114}{2849}} = \frac{2 \times 2849}{114} \] \[ \text{Average Speed} = \frac{5698}{114} \approx 49.98245 \text{ km/h} \]Alternatively, for a journey covering the same distance \(D\) at two different speeds \(S_1\) and \(S_2\), the average speed can be calculated using the formula:
\[ \text{Average Speed} = \frac{2 S_1 S_2}{S_1 + S_2} \]Using this formula:
\[ \text{Average Speed} = \frac{2 \times 37 \times 77}{37 + 77} \] \[ \text{Average Speed} = \frac{2 \times 37 \times 77}{114} \] \[ \text{Average Speed} = \frac{5698}{114} \approx 49.98245 \text{ km/h} \]Rounded to two decimal places, the average speed is 49.98 km/h.
B) 49.98 km/h
Washing soda is represented by Na2CO3.xH2O. The value of 'x' is equal to:
The question asks for the value of 'x' in the chemical formula of washing soda, which is given as \(\text{Na}_2\text{CO}_3\cdot\text{xH}_2\text{O}\). This requires knowledge of the common chemical formula for washing soda.
B) 10 is the correct value for 'x' as washing soda is chemically known as sodium carbonate decahydrate, meaning it contains 10 molecules of water of crystallization.
The problem involves finding the measure of the smaller of two supplementary angles. We know that supplementary angles add up to 180 degrees. We are also given a relationship between the two angles: the larger angle is 22 degrees more than the smaller angle. We can set up a system of two linear equations based on these two pieces of information and solve for the angles.
Define variables:
Let the smaller angle be \(x\) degrees.
Let the larger angle be \(y\) degrees.
Formulate the first equation (supplementary angles):
Since the angles are supplementary, their sum is 180 degrees.
Formulate the second equation (relationship between angles):
The problem states that the larger angle (\(y\)) is 22 degrees more than the smaller angle (\(x\)).
Solve the system of equations:
Substitute Equation 2 into Equation 1:
Simplify and solve for \(x\):
\[ 2x + 22^\circ = 180^\circ \]\[ 2x = 180^\circ - 22^\circ \]\[ 2x = 158^\circ \]\[ x = \frac{158^\circ}{2} \]\[ x = 79^\circ \]Find the larger angle (optional, but good for verification):
Substitute the value of \(x\) back into Equation 2:
Verify the sum:
\(x + y = 79^\circ + 101^\circ = 180^\circ\). This confirms our calculations are correct.
Identify the smaller angle:
The smaller angle is \(x\), which we found to be \(79^\circ\).
Correct Option: A) 79