54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :

Let us assume the two parts be y and (54 - y).
Then, According to question
10(54 - y) + 22y = 780
⇒ 540 - 10y + 22y = 780
⇒ 12y = 780 -540
⇒ 12y = 240
⇔ y = 20.
∴ Bigger part = (54 - y) = (54 - 20) = 34