$If 35^{2} - 27^{2} = 31 a,$
$then find the value of a.$

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Solution

The correct option is C 16
$Given : 35^{2} - 27^{2} = 31 a$

Using the identity,
$a^{2} - b^{2} = (a + b) (a - b)$

$35^{2} - 27^{2} = (35 + 27) (35 - 27)$
$\Rightarrow 31 a = (35 + 27) (35 - 27)$
$\Rightarrow 31 a = 62 \times 8$
$\Rightarrow a = 16$

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