Question

if (a-b ):(a+b) =1:11 then find (5a+4b+15):(5a-4b+3)

Answer 1

Answer :-

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Given ,

( a - b ) : ( a + b ) = 1 : 11

To find ,

The value of :- ( 5a + 4b + 15 ) : ( 5a - 4b + 3 )

Now ,

( a - b ) : ( a + b ) = 1 : 11

=> ( a - b ) / ( a + b ) = 1 / 11

=> 11a - 11b = a + b

=> 11a - a = b + 11b

=> 10a = 12b

=> 5a = 6b

=> a / b = 6 / 5

=> a : b = 6 : 5

Now let ,

a = 6k

b = 5k

[ • Where , k is a real number and k ≠ 0 ]

Therefore ,

( 5a + 4b + 15 ) : ( 5a - 4b + 3 )

= ( 5a + 4b + 15 ) / ( 5a - 4b + 3 )

= { 5 × 6k + 4 × 5k + 15 } / { 5 × 6k - 4 × 5k + 3 }

= ( 30k + 20k + 15 ) / ( 30k - 20k + 3 )

= ( 50k + 15 ) / ( 10k + 3 )

= 1 × ( 50k + 15 ) / ( 10k + 3 )

= 5 / 5 × ( 50k + 15 ) / ( 10k + 3 ) [ • Multiplying with 5 / 5 ]

= 5 ( 50k + 15 ) / 5 ( 10k + 3 )

= 5 ( 50k + 15 ) / ( 50k + 15 )

= 5 / 1

= 5 [ ★ Required answer ]

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★ Required answer ★