In a certain code language, 'RA + FE' is coded as ‘246', and 'AB + JC' is coded as ‘115'. How will 'AC + BD' be coded in that language?
37
This question asks us to decipher a specific code language where combinations of letters are assigned numerical values. We are given two examples of this coding pattern and need to apply the same logic to a new letter combination.
Let's carefully examine the examples provided to find the underlying rule:
We need to figure out how the letters 'RA', 'FE', 'AB', and 'JC' are converted into numbers and how the '+' symbol is used.
A common pattern in letter coding puzzles involves the alphabetical position of letters. Let's list the positions of the letters used in the examples:
Consider the first example: 'RA + FE' → '246'.
If we look at the positions of R (18) and A (1), and F (6) and E (5), how can we get 246?
Let's try combining the positions. What if the two letters before '+' form a number, and the two letters after '+' form another number, and these two numbers are added?
Let's add these concatenated numbers: $181 + 65 = 246$. This matches the first example!
Let's test this pattern with the second example: 'AB + JC' → '115'.
Let's add these concatenated numbers: $12 + 103 = 115$. This matches the second example as well!
The pattern is consistent. The rule is to take the alphabetical positions of the two letters in each pair, concatenate them to form a number, and then add the two resulting numbers.
| Letter Pair | Letter Positions | Concatenated Number | Calculation | Coded Value |
|---|---|---|---|---|
| RA | R=18, A=1 | 181 | $181 + 65 = 246$ | 246 |
| FE | F=6, E=5 | 65 | ||
| AB | A=1, B=2 | 12 | $12 + 103 = 115$ | 115 |
| JC | J=10, C=3 | 103 |
Now we apply the same rule to the expression 'AC + BD'.
First, find the alphabetical positions of the letters in 'AC':
Concatenate their positions to form a number: 13.
Next, find the alphabetical positions of the letters in 'BD':
Concatenate their positions to form a number: 24.
Finally, add the two numbers obtained:
Value of 'AC' + Value of 'BD' $= 13 + 24$.
Performing the addition:
$13 + 24 = 37$
Therefore, 'AC + BD' will be coded as '37' in this language.
| Step | Description | 'AC + BD' Application |
|---|---|---|
| 1 | Understand the problem and given examples. | Analyze 'RA+FE=246' and 'AB+JC=115'. |
| 2 | Identify the pattern by analyzing letter-to-number mapping. | Discover the concatenation of alphabetical positions. |
| 3 | Apply the identified pattern to the new expression. | Decode 'AC' and 'BD' using alphabetical positions. |
| 4 | Perform the required mathematical operation (addition in this case). | Add the values for 'AC' and 'BD'. |
| 5 | State the final coded value. | The result is 37. |
Letter coding puzzles often involve various patterns. Some common types include:
Solving these puzzles requires careful observation, logical reasoning, and testing different possible patterns based on the given examples.
A group of tourists from Australia visited New Delhi for sight-seeing. On a particular day, $\frac{1}{3}$ of them visited Qutub Minar, four times the square root of the total number of tourists visited Red Fort and the remaining 18 tourists were seen walking on the Kartavya Path near the India Gate. What is the total number of tourists who went out for sight-seeing on a particular day?
Anjali and Sanjana have some marbles with them. If Sanjana gives 15 marbles to Anjali, Anjali will have 10 marbles less than twice the marbles with Sanjana. If Sanjana gives 40 marbles to Anjali, Anjali will have 20 marbles more than three times the marbles with Sanjana. Find the number of marbles with Anjali.
If 1 is added to each even digit of the number 85624179 then the digits are arranged in ascending order from left to right. Find the product of the digits which are second from the left end and third from the right end.
In a certain code language, 'FALF' is written as 'HCJD'. How will 'OEMC' be written in that language?