Question

If four numbers are in A.P. such that their sum is $50$ and the greatest number is $4$ times the least, then the numbers are:

• A. $5,10,15,20$
• B. $4,10,16,22$
• C. $3,7,11,15$
• D. none of the above

Answer 1

The correct option is A $5,10,15,20$

Let the numbers be $a-3d,a-d,a+d,a+3d$
Given, sum of all the numbers:
$a-3d+a-d+a+d+a+3d=50$
$4a=50$
$a=12.5$
Given,
largest number = 4 (smallest number)
$a+3d=4a-12d$
$15d=3a$
$a=5d$
$d=\frac{12.5}{5}=2.5$
Therefore, numbers are $5,10,15,20$.