Question : The income of Raju is 25% more than that of Manju. Raju got a 25% rise in his income, and Manju got a 40% rise in his income, the percentage increase in their combined incomes is:
Option 1: 51.72%
Option 2: 31.67%
Option 3: 22.43%
Option 4: 41.26%
Correct Answer: 31.67%
Solution :
Let the income of Manju be 100.
The income of Raju is 25% more than Manju = 125
After increment of 25% in Raju's income = $125+\frac{25}{100}\times125=156.25$
After increment of 40% in Manju's income = $100+\frac{40}{100}\times100=140$
Their's combined previous income = 100 + 125 = 225
Their's combined new income = 140 + 156.25 = 296.25
$\therefore$ Required percentage
= $\frac{\text{Combined new income - Combined previous income}}{\text{Combined previous income}}\times100$
= $\frac{296.25-225}{225}\times100$
= $\frac{71.25}{225}\times100$
= $31.67\%$
Hence, the correct answer is 31.67%.
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