In a certain code language, 'PEPPER' is coded as 76 and 'CUCUMBER' is coded as 86. How will 'CAULIFLOWER' be coded in that language?
Decoding the Word Coding Pattern
This question presents a word coding problem where words are coded into numerical values. We are given two examples: 'PEPPER' coded as 76 and 'CUCUMBER' coded as 86. Our task is to find the code for 'CAULIFLOWER' using the same pattern.
Analyzing the Given Word Codes
Let's examine the provided examples to understand the coding rule. A common method in such problems is to assign numerical values to letters based on their position in the English alphabet (A=1, B=2, ..., Z=26) and then perform some operation (like summing, multiplying, etc.).
Coding of 'PEPPER'
Let's find the alphabetical position value for each letter in 'PEPPER':
- P = 16
- E = 5
- P = 16
- P = 16
- E = 5
- R = 18
Now, let's try summing these values:
$$ \text{Sum} = 16 + 5 + 16 + 16 + 5 + 18 $$ $$ \text{Sum} = 76 $$| Letter | Alphabetical Position |
|---|---|
| P | 16 |
| E | 5 |
| P | 16 |
| P | 16 |
| E | 5 |
| R | 18 |
| Total Sum | 76 |
The calculated sum is 76, which exactly matches the given code for 'PEPPER'.
Coding of 'CUCUMBER'
Let's apply the same method to 'CUCUMBER':
- C = 3
- U = 21
- C = 3
- U = 21
- M = 13
- B = 2
- E = 5
- R = 18
Let's sum these values:
$$ \text{Sum} = 3 + 21 + 3 + 21 + 13 + 2 + 5 + 18 $$ $$ \text{Sum} = 86 $$| Letter | Alphabetical Position |
|---|---|
| C | 3 |
| U | 21 |
| C | 3 |
| U | 21 |
| M | 13 |
| B | 2 |
| E | 5 |
| R | 18 |
| Total Sum | 86 |
The calculated sum is 86, which matches the given code for 'CUCUMBER'.
Based on the analysis of both examples, it appears the coding pattern is simply the sum of the alphabetical positions of all the letters in the word.
Calculating the Code for 'CAULIFLOWER'
Now we apply this established pattern to find the code for 'CAULIFLOWER'. Let's list the alphabetical position of each letter:
- C = 3
- A = 1
- U = 21
- L = 12
- I = 9
- F = 6
- L = 12
- O = 15
- W = 23
- E = 5
- R = 18
Next, we sum these values:
$$ \text{Sum} = 3 + 1 + 21 + 12 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$Let's add them step by step:
$$ \text{Sum} = 4 + 21 + 12 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 25 + 12 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 37 + 9 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 46 + 6 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 52 + 12 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 64 + 15 + 23 + 5 + 18 $$ $$ \text{Sum} = 79 + 23 + 5 + 18 $$ $$ \text{Sum} = 102 + 5 + 18 $$ $$ \text{Sum} = 107 + 18 $$ $$ \text{Sum} = 125 $$| Letter | Alphabetical Position |
|---|---|
| C | 3 |
| A | 1 |
| U | 21 |
| L | 12 |
| I | 9 |
| F | 6 |
| L | 12 |
| O | 15 |
| W | 23 |
| E | 5 |
| R | 18 |
| Total Sum | 125 |
The sum of the alphabetical positions of the letters in 'CAULIFLOWER' is 125.
Conclusion
Following the pattern observed in the examples, the code for 'CAULIFLOWER' is 125.
Revision Table: Word Coding Analysis
| Word | Letter Values (Alphabetical Position) | Sum of Values | Given Code | Pattern Match |
|---|---|---|---|---|
| PEPPER | 16, 5, 16, 16, 5, 18 | 76 | 76 | Yes |
| CUCUMBER | 3, 21, 3, 21, 13, 2, 5, 18 | 86 | 86 | Yes |
| CAULIFLOWER | 3, 1, 21, 12, 9, 6, 12, 15, 23, 5, 18 | 125 | ? | Predicted: 125 |
Additional Information: Word Coding Patterns
Word coding questions in reasoning often use various patterns beyond simple summing of alphabetical positions. Here are a few common types:
- Sum of position values: As seen in this problem (A=1, B=2, ...).
- Sum of reverse position values: (A=26, B=25, ...).
- Sum of position values with a constant addition/subtraction: The sum is calculated, and then a fixed number is added or subtracted.
- Sum based on vowels/consonants: Different rules or values might be applied to vowels and consonants.
- Position in alphabetical order within the word: Assigning values based on the order in which letters appear alphabetically within the specific word.
- Product of position values: Multiplying the values instead of summing them (less common for longer words due to large numbers).
- Combination of rules: A mix of the above, or more complex rules involving the number of letters, number of vowels, etc.
Solving these problems requires carefully analyzing the given examples to identify the specific rule being used.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
