Question

The sum of three numbers in A.P. is 30 and the ratio of first number to the third number is 3 : 7. Find the numbers.

Answer 1

Sum of three numbers in A.P. = 30
Ratio between first and the third number = 3 : 7
Let numbers be
a – d, a, a + d, then
a – d + a + a + d = 30
⇒ 3a = 30
⇒ a = `(30)/(3)` = 10
and
`"a - d"/"a + d" = (3)/(7)`
⇒ 7a – 7a = 3a + 3d
⇒ 7a – 3a = 3d + 7d
⇒ 4a = 10d
⇒ 10d = 4 x 10 = 40
⇒  d = `(40)/(10)` = 4
∴ Numbers are 10 – 4, 10, 10 + 4
⇒ 6, 10, 14.