Question

For a certain car repair, the total charge consisted of a charge for parts, a charge for labor, and a 6 percent sales tax on both the charge for parts and the charge for labor. If the charge for parts, excluding sales tax, was $50.00,whatwasthetotalchargefortherepair?\left(1\right)Thesalestaxonthechargeforlaborwas$9.60.
(2) The total sales tax was $12.60.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

Given that:
The charge for parts, excluding sales tax $=$\ 50$
Thus, the charge for parts, including sales tax

$\Rightarrow 50+Salestax\Rightarrow 50+6\%of50\Rightarrow 50+3\Rightarrow$\ 53 $
We have to get the total charge for the repair $=$ the charge for parts $+$ The charge for labor.
Statement 1:

The sales tax on the charge for labor was \ 9.60.$
Sales Tax $=\$9.60\Rightarrow 6\%$ of Charge for labour;
$9.60=\frac{6}{100}\times$ Charge for labour;
Charge for labor, excluding sales tax $\Rightarrow \frac{960}{6}\Rightarrow$\ 160.$
Charge for labor, including sales tax $\Rightarrow 160+9.60\Rightarrow$\ 169.60$
The total charge for the repair $=$ The charge for parts $+$ The charge for labor
$\Rightarrow 53+169.60\Rightarrow$\ 222.60$

Hence, statement 1 is Sufficient.
Statement 2:

The total sales tax was \ 12.60.$
The total sales tax $\Rightarrow 12.60\Rightarrow$ Sales tax on parts $+$ Sales tax on labour
We know that Sales tax on parts $=$\ 3,$

Thus,

Sales tax on labor $=12.60-3\Rightarrow$\ 9.60.$
Now, the information is the same as we get in Statement 1.

Hence,

Statement 2 is sufficient.

Conclusion: Each statement alone is sufficient.