An English word consists of 9 alphabets. The sum of twice the number of vowels and three times

the number of consonants present in the word is equal to four more than four times the total number of vowels in the English alphabets. The product of the number of vowels and consonants

present in the word is

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answer is C.

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Detailed Solution

Concept-
Here, we'll take the number of vowels as x and the number of consonants as y, and then, using the information in the question, we'll build the linear equations in two variables, solve them to determine the values of x and y, and then multiply the results to obtain the desired result.
Let the vowel count be x and the consonant count be y.
Given that there are a total of nine alphabets,
Thus, x+y=9_____(1)
Given that there are twice as many vowels and three times as many consonants in a word as there are vowels, there are more than four times as many vowels in the English alphabet. We are aware that the English alphabet has five vowels. As a result, by creating the necessary linear equation using the data above, we obtain:

https://lh6.googleusercontent.com/vOt8BNqBWjk_PAPtbpovOpAefx1Y8wfItnE1eWDZEP3JNuamDQa7G9x-dzJyeUJFifbgkU1Bj-oUp-iWKdy-bFOh8NwJBfxCSnZSqz0QnU0wVJdNFM27iOc7o-NlMmOBKW0UdoAMTrZCIl-n8EJqbg

To determine the values of x and y, we will now solve equations 1 and 2.
Equation 1 is multiplied by 2 to get

Subtracting equation 3 from 2,

Putting the value of y in equation 1

Now we need to calculate the product of the word's vowel and consonant counts.
Thus, in order to obtain the desired result, we must multiply the values of x and y.

Hence, the correct answer is option 3) 18

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