Question : The monthly salary of a person was INR 50,000. He spent on three heads—personal and family expenses (E), taxes (T), and philanthropy (P), and the rest were his savings. E was 50% of the income, T was 20% of E and P was 15% of T. When his salary was raised by 40%, he maintained the percentage level of E, but T became 30% of E and P became 20% of T. By what percentage is the new savings more or less than the earlier savings? (correct up to one decimal place)
Option 1: 16.4% more
Option 2: 8.2% less
Option 3: 8.2% more
Option 4: 16.4% less
Correct Answer: 16.4% more
Solution :
Let the total income of the person be 100.
Let E = expenditure, T = tax and P = philanthropy
E = 50
T = $50 \times \frac{20}{100} = 10$
P = $10 \times \frac{15}{100} = 1.5$
His savings = $100 - 50 - 10 - 1.5 = 38.5$
His new salary $=100 \times \frac{140}{100} = 140$
E $=140 \times \frac{50}{100} = 70$
T $=70 \times \frac{30}{100} = 21$
P $=21 \times \frac{20}{100} = 4.2$
New savings = $140 - 70 - 21 - 4.2 = 44.8$
His savings increased by = $\frac{44.8 - 38.5}{38.5}×100 =\frac{6.3}{38.5}\times 100= 16.4\%$
Hence, the correct answer is 16.4% more.
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