Question : If $a:b=5:7$, then $\left(6a^2-2b^2\right):\left(b^2-a^2\right)$ will be:
Option 1: 12 : 5
Option 2: 21 : 5
Option 3: 13 : 6
Option 4: 17 : 8
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Correct Answer: 13 : 6
Solution :
$a: b=5: 7$
Assume $a$ as 5 and $b$ as 7.
$(6a^2-2b^2):(b^2-a^2)$
$= (6×5^2-2×7^2):(7^2-5^2)$
$= (6×25-2×49):(49-25)$
$= (150-98):(49-25)$
$= 52:24$
$= 13:6$
Hence, the correct answer is 13 : 6.
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