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

Correct  answer is A. 5,10,15,20

Let the 4 numbers be a, a + d, a + 2d, a + 3d. 

Sum of 4 numbers in A.P = 50 

a + a + d + a + 2d + a + 3d = 50 

⇒ 4a + 6d = 50 

⇒ 2a + 3d = 25 --------------(1) 

Given the greatest number is 4 times the least. 

4(a) = a + 3d 

4a – a = 3d 

a = d

Putting, a = d in (1), we obtain 

5d = 25 

d = 5 

⇒ a = 5 

∴ First four terms are 5, 10, 15, 20.