By how much is 60% of 40 greater than \( \frac{1}{5} \) of 15?
To find out by how much 60% of 40 is greater than \( \frac{1}{5} \) of 15, we need to calculate both values separately and then find their difference.
To find a percentage of a number, convert the percentage to a decimal or a fraction and multiply it by the number.
\[ 60\% \text{ of } 40 = \frac{60}{100} \times 40 \]\[ = \frac{6}{10} \times 40 \]\[ = 6 \times 4 \]\[ = 24 \]To find a fraction of a number, multiply the fraction by the number.
\[ \frac{1}{5} \text{ of } 15 = \frac{1}{5} \times 15 \]\[ = \frac{15}{5} \]\[ = 3 \]Subtract the second value from the first value to find out by how much the first value is greater.
\[ \text{Difference} = 24 - 3 \]\[ = 21 \]Therefore, 60% of 40 is greater than \( \frac{1}{5} \) of 15 by 21.
Correct Option: B) 21
To determine the rate of increase in capital expenditure, we need the capital expenditure figures for the central government on major infrastructure sectors for the financial years 2019-20 and 2023-24. Once these figures are known, the percentage increase can be calculated using the standard formula for percentage change.
\[ \text{Absolute Increase} = \text{Expenditure}_{2023-24} - \text{Expenditure}_{2019-20} \]
\[ \text{Absolute Increase} = ₹7.6 \text{ lakh crore} - ₹5.5 \text{ lakh crore} = ₹2.1 \text{ lakh crore} \]
\[ \text{Percentage Increase} = \left( \frac{\text{Absolute Increase}}{\text{Expenditure}_{2019-20}} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{₹2.1 \text{ lakh crore}}{₹5.5 \text{ lakh crore}} \right) \times 100 \]
\[ \text{Percentage Increase} = 0.3818 \times 100 \approx 38.18\% \]
A) 39% is the correct option as the calculated rate of increase is approximately 38.18%, which rounds to 39%.
This is a linear arrangement puzzle. We need to deduce the seating arrangement of seven friends based on the given clues. We will place the friends one by one, starting with the most restrictive clues, and build the arrangement.
Clue 1: No one sits to the right of E.
Since all are facing North, "right" is the rightmost position. This means E is at the extreme right end of the row of 7 people.
_ _ _ _ _ _ E
Clue 2: Only two people sit between E and P.
Counting two positions to the left of E, we place P.
_ _ _ _ P _ E
Clue 3: P sits to the immediate left of C.
This means C is immediately to the right of P.
_ _ _ _ P C E
Clue 4: Only three people sit between F and C.
We have C in the 6th position. Counting three places to the left of C, we find F.
F _ _ P C E
Now, let's combine the arrangement and count the total positions filled. We have 6 positions filled: F _ _ P C E. There are 7 friends in total, so one position is still empty. The empty slot is between F and P.
F _ _ P C E becomes F _ _ P C E. The missing person must be placed in the first empty slot.
Let's re-evaluate the positions: F (1) _ (2) _ (3) P (4) C (5) E (6). This is only 6 people. The total is 7. So, the arrangement must be:
F _ _ _ P C E
Let's re-check the "three people between F and C" with this arrangement:
F (1) _ (2) _ (3) _ (4) P (5) C (6) E (7)
This means there are three people between F and C. This fits the clue. The current arrangement is:
F _ _ _ P C E
Clue 5: H sits to the immediate right of D.
We have two empty slots. The remaining friends are G, D, H. The only way to place D and H together is in the remaining two consecutive slots.
D H _ P C E
The remaining person is G. The only empty slot is the one between H and P.
D H G P C E
Let's verify all clues with the final arrangement:
Let's start fresh with the most solid clues.
E is at the extreme right: _ _ _ _ _ _ E
Two people between E and P: _ _ _ _ P _ E
P is to the immediate left of C: _ _ _ _ P C E
Three people between F and C. C is at position 6. Counting 3 people to its left means F is at position 2 (6 - 3 - 1 = 2)._ F _ _ P C E (This is 6 people. We need 7. So F must be at the very left end, and there are 3 people between F and C).
Let's assume the positions are 1 2 3 4 5 6 7.
E is at 7: _ _ _ _ _ _ E
Two people between E (7) and P. So P is at 4: _ _ _ P _ _ E
P is to the immediate left of C. So C is at 5: _ _ _ P C _ E
Three people between F and C. C is at 5. Counting 3 people to the left of C, F must be at position 1: F _ _ P C _ E
The arrangement is now: F _ _ P C _ E. This accounts for 6 positions. The missing position is 6.
Let's re-read "Only three people sit between F and C".
If F is at 1, and C is at 5, then there are 3 people (positions 2, 3, 4) between F and C. This is correct.
So the arrangement is: F _ _ P C _ E
We have 7 positions. The filled ones are F(1), P(4), C(5), E(7). The empty ones are 2, 3, 6.
The remaining friends are D, G, H.
H sits to the immediate right of D. This means D and H must occupy two consecutive empty slots. The only consecutive empty slots are 2 and 3.
So, D is at 2, H is at 3.
The arrangement becomes: F D H P C _ E
The last remaining friend is G. The last empty slot is 6.
So, G is at 6.
The final arrangement is: F D H P C G E
Question: How many people sit between G and H?
From the final arrangement: F D H P C G E
H is at position 3, G is at position 6.
The people between H and G are P and C.
There are two people (P and C) between G and H.
B) Two — As determined from the final arrangement F D H P C G E, there are two people (P and C) between G and H.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to analyze the relationship between the letters in each pair based on their positions in the English alphabet.
Option A does not follow this pattern:
The difference between the letters within each cluster is not 3, and the relationship between the corresponding letters of the two clusters is not a consistent +3.
A) MH - KJ — In this option, the difference between the letters in the first cluster (M, H) is \(13 - 8 = 5\), and in the second cluster (K, J) is \(11 - 10 = 1\). This does not match the pattern of a difference of 3 found in the other options. Also, the relationship between corresponding letters (M to K is \(13-11=2\), H to J is \(8-10=-2\)) is not consistent.
The question asks to identify the Indian National Congress (INC) session where resolutions opposing the Arms Act and the Vernacular Press Act were passed. This requires knowledge of the early history of the INC and the specific resolutions passed at its initial sessions.
Correct Option: B) 1885 Bombay
The first session of the Indian National Congress, held in Bombay in 1885, passed several resolutions. Among these were resolutions expressing strong disapproval of the Arms Act and the Vernacular Press Act, both of which were seen as discriminatory and repressive by Indian nationalists.
To solve this problem, we need to identify the highest and lowest numbers from the given set of three-digit numbers. Then, we will extract the second digit from each of these identified numbers and perform the subtraction as specified in the question.
The resultant is \(-2\).
Correct Option: D) \(-2\)
The problem asks us to find the mode of a data set given its mean and median, using the empirical relation between these three measures of central tendency. The empirical relation states that for a moderately skewed distribution, the difference between the mean and mode is approximately three times the difference between the mean and median.
Recall the empirical relation: The empirical relationship between mean, median, and mode for a moderately skewed distribution is given by:
\[ \text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean} \]Identify the given values:
Substitute the values into the formula:
\[ \text{Mode} \approx 3 \times (78) - 2 \times (43) \]Calculate the products:
Perform the subtraction to find the mode:
\[ \text{Mode} \approx 234 - 86 \]\[ \text{Mode} \approx 148 \]Correct Option: C) 148
The mode of the data, calculated using the empirical relation, is 148.
The problem presents an analogy between letter-clusters. We need to find the pattern or relationship between the first pair of letter-clusters and apply the same logic to the second pair to find the missing clusters.
A) # = KUG, % = FPB
As determined in the step-by-step analysis, if we assume the pattern is adding 10 to the alphabetical position of each letter (cyclically), then KUG becomes UEQ and VFR becomes FPB. This option perfectly fits the derived pattern.
To find the speed of the man in still water, we first need to calculate his speed downstream and upstream. We can then use the formulas relating these speeds to the speed of the man in still water and the speed of the current.
B) The speed of the man in still water is 9 km/hr.
The question asks to identify the folk song from Kerala that is sung to ward off evil spirits. This requires knowledge of specific folk traditions and their associated names.
B) Bhuta — The term 'Bhuta' (often associated with 'Bhuta Kola' or 'Bhuta Aradhane') refers to a ritualistic folk tradition prevalent in parts of Kerala and Karnataka, which involves elaborate performances, music, and dances to appease or send away spirits and deities. The songs sung during these rituals are integral to the process of warding off evil.