A person earns:
- Current daily earnings: $\(\$ 100\)$ by working 10 hours at $\(\$ 10\)$ per hour.

We need to compare:
- Quantity A: Earnings per day if the hourly wage is increased by $\(\mathbf{4 0 \%}\)$ (working the same 10 hours).
- Quantity B: Earnings per day if working hours are increased by $\(10 \%\)$ and hourly wage is increased by 30\%.

Step 1: Calculate Quantity A
- Current hourly wage: \(\$10\)
- Increase in hourly wage by $\(40 \%\)$ :

New hourly wage $\(=10+(10 \times 0.40)=\$ 14\)$
- Earnings for 10 hours:

Quantity $\(\mathrm{A}=14 \times 10=\$ 140\)$
Step 2: Calculate Quantity B
- Current working hours: 10
- Increase in working hours by $\(10 \%\)$ :

New working hours $\(=10+(10 \times 0.10)=11\)$ hours
- Current hourly wage: $\(\$ 10\)$
- Increase in hourly wage by $\(30 \%\)$ :

New hourly wage $\(=10+(10 \times 0.30)=\$ 13\)$
- Earnings for 11 hours:

Quantity $\(B=13 \times 11=\$ 143\)$
Step 3: Compare Quantity A and Quantity B
- Quantity A:\( \$140\)
- Quantity B: $\(\$ 143\)$

Conclusion
Quantity B > Quantity A