Question

If four numbers in A.P. are 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 these

Answer 1

Answer: (A)

5, 10, 15, 20

Let the four numbers in A.P. be as follows:

$a-2d,a-d,a,a+d$

Their sum = 50 (Given)

$\Rightarrow (a-2d)+(a-d)+a+(a+d)=50$

$\Rightarrow 2a-d=25\dots \dots \left(i\right)$

Also, $(a+d)=4(a-2d)$

$\Rightarrow a+d=4a-8d$

$\Rightarrow 3d=a\dots \dots \left(ii\right)$

From equations (i) and (ii), we get

$d=5,a=15$

Hence, the numbers are $15-10,15-5,15,15+5,$ i.e., $5,10,15,20.$