Let four numbers in A.P. are
a, a + d, a + 2d, a + 3d
According to question
a + (a + d) + (a + 2d) + (a + 3d) = 50
⇒ 4a + 6d = 50
⇒ 2(2a + 3d) = 50
⇒ 2a + 3d = 25 …..(i)
If larger number is 4 times the smaller number, then equation will be as follow,
a + 3d = 4 x a
⇒ a + 3d = 4a
⇒ 3d = 3a
⇒ d = a …(ii)
from equation (i) and (ii)
2a + 3a = 25 [∴ d = a]
a = 25
a = 5
∴ d = 5 [∵ eqn(ii)]
∴ Numbers a = 5
a + d = 5 + 5 = 10
a + 2d = 5 + 2 × 5 = 15
a + 3d = 5 + 3 × 5 = 20
Hence, four numbers are 5, 10, 15, and 20
