Question # If ( x ) varies inversely as ( left(y^{2}-1right) ) and is equal to 24 when ( y=10 ), then the value of ( x ) when ( y=5 ) is:

# If ( x ) varies inversely as ( left(y^{2}-1right) ) and is equal to 24 when ( y=10 ), then the value of ( x ) when ( y=5 ) is:

( (A) 99 )

(B) 12

(C) 24

(D) 100

Solution

( frac{x}{y^{2}-1} Rightarrow x=frac{k}{y^{2}-1} )

Put ( x=24, y=10 )

( 24=frac{k}{100-1}=frac{k}{99} )

( x=24 times 99 )

Put ( y=5 )

( x=frac{k}{25-1}=frac{24 times 99}{24}=99 . quad )

Option (A)