What is the Cost Price of a Commodity which has a Loss of 2%

Question

When a commodity is sold for \$34.80, thre is a loss of 2%. What is the cost price of the commodity?

The answer choices are as follow:

\$26.10

\$43

\$43.20

\$46.40

I tried to solve this by multiplying 34.80 dollars to 98 percent
(since there is a loss of 2%) and get $34.104.

But the answer key states that the answer is \$46.40.

Cost Price = (100/75 x 34.80) which yields \$46.40.

I don't know how it ended up with 100/75 in the solution, or how there's even 75 in it. I suspect the problem has some kind of typographical error.. Or if none, how did it wind up as $46.40?

Please help me understand this problem and reconcile the problem itself, the answer key I have and the solution I made earlier. (My suspicion is that it has a typo error. It has a 25% loss not 2%.)

PS I am a first yr college student struggling with word problems, specifically.

Thank you!

Answer 1

$$\frac{34.8}{x}=\frac{98}{100}\implies x=\frac{34.8}{0.98}$$

Answer 2

Yes, it must be a typo in the problem statement.

It makes no sense as written (with the given answers), but if we assume that the digit 5 has simply gone missing, both one of the answer options and the working in the answer key makes sense.

Answer 3

If the loss is $2\%$, then you would need to divide by $0.98$. If the cost is $C$ then you have $$ \$34.80 = (98\% \text{ of }C)= 0.98C. $$ So $$ C=\frac{\$34.80}{0.98}. $$ However, it does appear that $25\%$ rather than $2\%$ was intended.