54 is to be divided into two parts such that the sum of

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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 :

1. 24
2. 34
3. 30
4. 32

Correct Option: B

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