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A person earns $100 in a day, working for 10 hours at $10 per hour.
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21 May 2025, 13:42
21 May 2025, 13:42
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A person earns $100 in a day, working for 10 hours at $10 per hour.
Quantity A |
Quantity B |
Earnings per day, if hourly wage is increased by 40% for working 10 hours |
Earnings per day, if working hours increased by 10% and hourly wage increased by 30% |
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Re: A person earns $100 in a day, working for 10 hours at $10 per hour.
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23 May 2025, 04:30
23 May 2025, 04:30
Expert Reply
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
- 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
gmatclubot
Re: A person earns $100 in a day, working for 10 hours at $10 per hour. [#permalink]
23 May 2025, 04:30
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