If ( a / 2 ) = ( b / 3 ) = ( c / 4 ) = ( 2a – 3b + 4c ) / ( p ), then find p.

Given : ( a / 2 ) = ( b / 3 ) = ( c / 4 ) = ( 2a – 3b + 4c ) / ( p ) = k ( Say ) .
∴ a = 2k
b = 3k
c = 4k
and 2a – 3b + 4c = pk
⇒ 2 ( 2k ) – 3 ( 3k ) + 4 ( 4k ) = pk
⇒ 4k – 9k + 16k = pk
⇒ 11k = pk
⇒ 11 = p
∴ p = 11

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