Question

If $2(a-8\times 5)-2\times 7=3\times 1\times a+7\times 4-(8\times 1\times a-1)$, find $a$.

• A. $\frac{123}{8}$
• B. $\frac{123}{7}$
• C. $\frac{8}{123}$
• D. $\frac{7}{123}$

Answer 1

Answer: (B)

$\frac{123}{7}$

Given, $2(a-8\times 5)-2\times 7=3\times 1\times a+7\times 4-(8\times 1\times a-1)$.

L.H.S.

$=2\times a-2\times 8\times 5-2\times 7$
$=2a-80-14$ ...[Simplifying]
$=2a-94$.

R.H.S.

$=3\times 1\times a+7\times 4-(8\times 1\times a-1)$

$=3a+28-8a+1$...[Simplifying]

$=-5a+29$.

According to the question, L.H.S. $=$ R.H.S.

Then,
$\Rightarrow 2a-94=-5a+29$.

Transposing $a$ terms to one side, we get,

$\Rightarrow 2a+5a=94+29$

$\Rightarrow 7a=123$

$\Rightarrow a=\frac{123}{7}$.

Hence, option $B$ is correct.