If a student multiplied a number by \( \frac{3}{4} \) instead of \( \frac{4}{3} \), then find the percentage of error in that calculation (approximate).
To find the percentage error, we first need to determine the correct value and the incorrect value obtained due to the multiplication error. Then, we calculate the absolute error and express it as a percentage of the correct value.
Assume a number: Let the number be \(X\). For simplicity in calculation, we can choose a number that is a multiple of the denominators of the fractions involved, i.e., a multiple of 4 and 3. Let's choose \(X = 12\).
Calculate the correct value: The student should have multiplied the number by \( \frac{4}{3} \).
Correct Value \[= X \times \frac{4}{3} = 12 \times \frac{4}{3} = 4 \times 4 = 16\].
Calculate the incorrect value: The student actually multiplied the number by \( \frac{3}{4} \).
Incorrect Value \[= X \times \frac{3}{4} = 12 \times \frac{3}{4} = 3 \times 3 = 9\].
Calculate the absolute error: The error is the difference between the correct value and the incorrect value.
Absolute Error \( = | \text{Correct Value} - \text{Incorrect Value} | = |16 - 9| = 7 \).
Calculate the percentage error: Percentage error is calculated as \[\frac{\text{Absolute Error}}{\text{Correct Value}} \times 100\%\].
\[ \text{Percentage Error} = \frac{7}{16} \times 100\% \]\[ \text{Percentage Error} = 0.4375 \times 100\% \]\[ \text{Percentage Error} = 43.75\% \]
Approximate the result: The approximate percentage error is 44%.
B) 44% is the calculated approximate percentage error.
To find the least number that is exactly divisible by a set of given numbers, we need to calculate the Least Common Multiple (LCM) of those numbers. The LCM is the smallest positive integer that is a multiple of all the numbers.
Thus, the least number exactly divisible by 12, 16, 24, and 32 is 96.
C) 96 — As calculated, the LCM of 12, 16, 24, and 32 is 96. This means 96 is the smallest number that can be divided by all these numbers without leaving a remainder.
To solve this problem, we need to first calculate the initial speed of the bus. Then, we will decrease this speed by the given amount to find the new speed. Finally, we will use the new speed and the same distance to calculate the new time taken.
Given:
First, convert the time from minutes to hours:
\[ T = 20 \text{ min} = \frac{20}{60} \text{ hr} = \frac{1}{3} \text{ hr} \]Now, calculate the speed using the formula \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\):
\[ \text{Initial Speed} = \frac{5 \text{ km}}{\frac{1}{3} \text{ hr}} = 5 \times 3 \text{ km/hr} = 15 \text{ km/hr} \]The speed is decreased by \(3 \text{ km/hr}\).
\[ \text{New Speed} = \text{Initial Speed} - 3 \text{ km/hr} = 15 \text{ km/hr} - 3 \text{ km/hr} = 12 \text{ km/hr} \]The distance remains the same, \(D = 5 \text{ km}\).
Using the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\):
\[ \text{New Time} = \frac{5 \text{ km}}{12 \text{ km/hr}} = \frac{5}{12} \text{ hr} \]Convert the new time from hours to minutes:
\[ \text{New Time} = \frac{5}{12} \times 60 \text{ min} = 5 \times 5 \text{ min} = 25 \text{ min} \]A) 25 min — As calculated, the new time taken by the bus to cover the same distance is 25 minutes.
This is a coding-decoding problem. We need to identify the pattern or rule used to assign numerical values to letters and then apply that rule to the word "FASHION".
In standard alphabetical order, A is the 1st letter and H is the 8th letter. The given values (26 for A, 19 for H) suggest a reverse alphabetical order coding where Z=1, Y=2, ..., A=26. Let's verify this:
The pattern is confirmed: each letter is assigned its position in the alphabet when counted backward from Z (Z=1, Y=2, ..., A=26).
FASHION = 21 26 8 19 18 12 13
Correct Option: A) 2126819181213
The question gives the number of days Rajesh and Mahesh take to complete the same task individually. Since they work together, their payment should be divided in proportion to their individual work rates. We need to calculate the ratio of their efficiencies and use it to determine Rajesh's share of the total payment.
Identify the given information:
Calculate the individual work rates:
Rajesh completes the entire task in 4 days.
Therefore, his one-day work is:
\[ \frac{1}{4} \]Mahesh completes the entire task in 3 days.
Therefore, his one-day work is:
\[ \frac{1}{3} \]Determine the ratio of their work:
Since both work together for the same duration, the ratio of their contributions is equal to the ratio of their one-day work rates.
\[ \text{Rajesh : Mahesh}=\frac{1}{4}:\frac{1}{3} \]Multiplying both terms by the LCM of 4 and 3, which is 12:
\[ =\frac{1}{4}\times12:\frac{1}{3}\times12 \] \[ =3:4 \]Therefore, Rajesh and Mahesh should divide the payment in the ratio 3:4.
Calculate Rajesh's share:
Total number of parts:
\[ 3+4=7 \]Rajesh receives 3 parts out of 7.
\[ \text{Rajesh's Share}=\frac{3}{7}\times350 \] \[ =3\times50 \] \[ =150 \]Therefore, Rajesh's share is ₹150.
Correct Option: B) ₹150 — Rajesh and Mahesh complete the task individually in 4 days and 3 days, respectively. Their work rates are in the ratio:
\[ \frac{1}{4}:\frac{1}{3}=3:4 \]
Therefore, Rajesh's share of the total payment is:
\[ \frac{3}{3+4}\times350=150 \]
Hence, Option B is the correct answer.
A) ₹100: This is incorrect because Rajesh contributes 3 out of 7 parts of the total work, giving him ₹150 rather than ₹100.
C) ₹200: This is incorrect because ₹200 is Mahesh's share, as he contributes 4 out of 7 parts of the total work.
D) ₹140: This is incorrect because the payment must be divided in the work ratio 3:4, which gives Rajesh ₹150, not ₹140.
The problem presents a coding-decoding puzzle where letters are assigned numerical values. We need to identify the pattern used to assign these values and then apply it to find the code for "EDITION".
Let's consider the alphabetical position of each letter (A=1, B=2, ..., Z=26).
This suggests a pattern where the code for a letter is \(27 - \text{alphabetical position of the letter}\). This is a common coding technique where each letter is replaced by its reverse alphabetical order counterpart (e.g., A becomes Z, B becomes Y, etc., and their positions sum to 27).
We will find the alphabetical position for each letter in "EDITION" and then subtract it from 27.
Concatenating these codes in order gives: 2223187181213.
Correct Option: B) 2223187181213
Find the mean of the following distribution.
| x: | 5 | 6 | 7 | 8 | 9 |
| f: | 4 | 8 | 14 | 11 | 3 |
To find the mean of a discrete frequency distribution, we use the formula for the arithmetic mean, which is the sum of the products of each observation (\(x\)) and its corresponding frequency (\(f\)), divided by the sum of all frequencies.
We are given the values of \(x\) (observations) and \(f\) (frequencies) as follows:
The mean (\(\bar{x}\)) is given by:
\[ \bar{x} = \frac{\sum fx}{\sum f} \]Substitute the calculated values:
\[ \bar{x} = \frac{281}{40} \] \[ \bar{x} = 7.025 \]Correct Option: C) 7.025
The question asks to identify the 'Father of Indian Cinema'. This requires knowledge of prominent figures in the history of Indian cinema and their contributions.
Dadasaheb Phalke produced India's first full-length feature film, Raja Harishchandra, in 1913. His pioneering efforts laid the foundation for the Indian film industry, earning him the title 'Father of Indian Cinema'.
C) Dadasaheb Phalke — Dhundiraj Govind Phalke, popularly known as Dadasaheb Phalke, is widely regarded as the 'Father of Indian Cinema'. He directed India's first full-length feature film, Raja Harishchandra, in 1913, and was instrumental in establishing the film industry in India.
The question asks to identify the founding father of Macroeconomics as a separate discipline. This requires knowledge of key figures in economic thought and their contributions to the field.
C) John Maynard Keynes is considered the founding father of macroeconomics as a separate discipline. His work, especially "The General Theory of Employment, Interest and Money" (1936), provided a comprehensive framework for understanding aggregate economic phenomena such as national income, employment, and inflation, and laid the groundwork for government intervention to stabilize the economy. This marked a significant departure from classical economic thought, which primarily focused on microeconomic issues and assumed full employment.
The question asks to identify a single-chip device that functions as a complete processor and can perform arithmetic and logical operations. We need to evaluate each option based on its definition and functionality in the context of computer hardware.
C) Microprocessor — A microprocessor is indeed a single-chip device that acts as the central processing unit (CPU) of a computer, capable of executing instructions, performing arithmetic calculations, and logical operations. It is the "brain" of most digital electronic devices.