Question

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

• A. 5, 10, 15, 20
• B. 4, 10, 16, 22
• C. 3, 7, 11, 15
• D. None of these

Answer 1

Answer: (A)

5, 10, 15, 20

Let the four number in A.P
$a-3d,a-d,a+d,a+3d$
Then according to the question
$a-3d+a-d+a+d+a+3d=50$
$4a=50$
$a=\frac{50}{4}=\frac{25}{2}$
$a+3d=4(a-3d)$
$a-4a=-3d-12d$
$-3a=-15d$
$d=\frac{3a}{15}$
$d=\frac{3\times \frac{25}{2}}{15}=\frac{5}{2}$
Hence, the four numbers are $5,10,15,20$.