Three consecutive integers when taken in increasing order and multiplied by 2, 3 and 4 respectively adds up to 74. What is the greatest number?

Correct option is A

Given:

Three numbers are consecutive.

Solution:

Let the three consecutive integers be x, x+1, and x+2.

The first integer is multiplied by 2.
The second integer is multiplied by 3.
The third integer is multiplied by 4.

The sum of these three terms is equal to 74.

According to question
2x + 3(x+1) + 4(x+2) = 74
2x + 3x + 3 + 4x + 8 = 74
9x + 11 = 74
9x = 74 - 11 = 63
x = $$\frac{63}{9}$$​= 7
Third integer: x + 2 = 9
Thus, the greatest number is:9