This is a classic percent problem that trips up a lot of students. The tricky part? You need to recognize that when Mrs. Lee's income increases but everyone else's stays the same,
both her earnings AND the total family income change. Let me walk you through how to handle this.
Here's how to think about it:Step 1: Understand what's happeningIn May, Mrs. Lee earned 60% of the family's total income. That means the rest of the family earned 40%. In June, Mrs. Lee got a 20% raise on her May earnings, while everyone else's income stayed exactly the same. You need to find what percent of the
new total her June earnings represent.
The key insight here: When Mrs. Lee's income goes up but the rest stays constant, the family's total income increases too. So you can't just add 20% to 60% and call it a day!
Step 2: Use concrete numbersLet's make this easier by using actual dollar amounts. Since Mrs. Lee earned 60% of the total in May, let's say the family's total income in May was $100.
So in May:
- Mrs. Lee: $60 (60% of $100)
- Rest of family: $40 (40% of $100)
- Total: $100
Step 3: Calculate June earningsMrs. Lee earned 20% more in June than in May:
\(20\%\) of \(\$60 = \$12\)
So Mrs. Lee's June earnings: \(\$60 + \$12 = \$72\)
Step 4: Find the new percentageNow here's where students often slip up. The rest of the family still earned $40, so:
June family income:
- Mrs. Lee: $72
- Rest of family: $40
- New total: $112
Mrs. Lee's percentage in June:
\(\frac{72}{112} = 0.6429 = 64.29\%\)
Approximately
64%Answer: (A) 64%Notice how Mrs. Lee's share only went from 60% to about 64%, not to 80%? That's because the denominator (total family income) increased along with her earnings.
Want to master these "changing base" percent problems? The complete solution on Neuron shows you the systematic framework that works every time, plus the common trap variations of this problem type and time-saving techniques. You can check out the
step-by-step solution on Neuron by e-GMAT to understand the underlying pattern recognition approach. You can also practice with comprehensive solutions for
other official questions here to build consistent accuracy on these problem types.
Hope this helps!