Question

If four numbers are in A.P. such that their sum is 60 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 these

Answer 1

The correct option is D None of these

Let the four numbers be $a,a+d,a+2d,a+3d$.

The sum of four numbers$=4a+6d=60$

$\Rightarrow$ $2a+3d=30$

Given that the largest number is four times the smaller one.

$\Rightarrow$ $a+3d=4a$

$\Rightarrow$ $a=d$

$\Rightarrow$ $5d=30$. (From $2a+3d=30$)

$\Rightarrow$ $d=6$

Therefore, numbers are $6,12,18,24$

Therefore, Option D is correct.