If the sum of one-half and one-fifth of the number exceeds one-third of that number by 7 1/3 , the number is

Let us assume the number is a.
Given that 7 ¹/3 = 22/3
According to question,
a x 1/2 + a x 1/5 = a x 1/3 + 22/3
⇒ a/2 + a/5 = a/3 + 22/3
⇒ a/2 + a/5 - a/3 = 22/3
⇒ (15a + 6a - 10a)/30 = 22/3
⇒ (15a + 6a - 10a) = 30 x 22/3
⇒ 11a = 10 x 22
⇒ a = 10 x 2
⇒ a = 20