Understanding the Problem
We have a person who currently:
- Works 10 hours a day.
- Earns \$10 per hour.
- Therefore, earns \$100 per day (since 10 hours * \$10/hour = \$100).

Now, we have two scenarios to calculate new daily earnings:
Quantity A:
- Hourly wage is increased by $40 \%$, still working 10 hours.

Quantity B:
- Working hours increased by $10 \%$, and hourly wage increased by $30 \%$.

We need to calculate the earnings per day for both scenarios and then compare Quantity A and Quantity B.

Calculating Quantity A
Current hourly wage: $\$ 10$
Increase by 40\%: 40\% of \$10 = $0.40 * \$ 10=\$ 4$
New hourly wage: $\$ 10+\$ 4=\$ 14$
Hours worked: 10 hours
Earnings per day (Quantity A):
= New hourly wage * Hours worked
$=\$ 14 /$ hour $* 10$ hours
$=\$ 140$

Calculating Quantity B
Current hours worked per day: 10 hours
Increase by 10\%: 10\% of 10 hours = $0.10 * 10=1$ hour
New hours worked per day: 10 hours + 1 hour = 11 hours
Current hourly wage: $\$ 10$
Increase by 30\%: 30\% of \$10 = $0.30 * \$ 10=\$ 3$
New hourly wage: $\$ 10+\$ 3=\$ 13$
Earnings per day (Quantity B):
= New hourly wage * New hours worked
= \$13/hour * 11 hours
= \$143
Comparing Quantity A and Quantity B
- Quantity A: \$140
- Quantity B: $\$ 143$

Now, let's compare the two:
- \$140 (Quantity A) vs. \$143 (Quantity B)

Clearly, $\$ 143$ is greater than $\$ 140$, so Quantity B is greater than Quantity A.

Verifying the Calculations
Let me double-check the calculations to ensure no mistakes were made.
Quantity A:
- $40 \%$ increase on $\$ 10$ : $\$ 10 * 1.40=\$ 14$
- 10 hours * $\$ 14=\$ 140$.

Quantity B:
- $10 \%$ increase on 10 hours: $10 * 1.10=11$ hours
- $30 \%$ increase on $\$ 10$ : $\$ 10 * 1.30=\$ 13$
- 11 hours $* \$ 13=\$ 143$.

The calculations seem correct.
Considering Alternative Interpretations
Is there any other way to interpret the problem that might lead to a different answer?

The wording seems clear:
- For Quantity A: Only the hourly wage increases by $40 \%$, hours remain the same.
- For Quantity B: Both hours and hourly wage increase by $10 \%$ and $30 \%$ respectively.

No ambiguity seems present in the phrasing.

Final Answer
After carefully calculating both quantities:
- Quantity A: $\$ 140$
- Quantity B: $\$ 143$

Quantity B is greater than Quantity A .
$B$ (Quantity B is greater)