Question

The sum of three numbers is 92. The second number is three times the first and the third exceeds the second by 8. The three number are:
$A.$ 14, 36, 42
$B.$ 18, 30, 44
$C.$ 8, 38, 46
$D.$ 12, 36, 44

Answer 1

Hint:Take the first number as ’x’. Thus, find the second and third number with the given information. Add three 3 numbers and equate it to 92. Thus, get the value of x and first the 3 numbers.

Complete step-by-step answer:
It is given that the sum of three numbers is 92.
Let us consider the first number as ‘x’.
It is said that the second number is three times the first. Thus, the 2nd number = 3x.
The third number exceed the second number by 8
$\therefore $ Third number = second number + 8
= 3x + 8
 Thus, the three numbers are x, 3x, (3x + 8). Their sum in 92.
$\therefore $ x + 3x +(3x + 8) = 92
7x + 8 = 92
7x = 92 – 8
7x = 84
$\therefore x=\dfrac{84}{7}=12$
Thus, we got the 1st number = x = 12
Second number $=3x=3\times 12=36$.
Third number = 3x + 8 = $3\times 12+8$ = 36 + 8 = 44
Thus, we got the three numbers as 12, 36, 44.
$\therefore $ option (D) is the correct answer.
Note: Students sometimes add each option given to make sure if the sum is 92 But it is wrong here all of their sum is 92,you have to consider the numbers as x, 3x, (3x + 8) in order to solve the given equation.