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

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

Solution:

(a) 5, 10, 15, 20

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

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

Their sum = 50 (Given)

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

$\Rightarrow 2 a-d=25$

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

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

$\Rightarrow 3 d=a$   ....(2)

From equations 1 and 2,">(1) and (2), we get:

d  = 5, a = 15

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