Ravi spends 75% of his income. His income rises by 20% and his spending by 10%. By what percentage do his savings increase?
By 50%. Take income 100, spending 75, savings 25. New income 120, new spending 82.5, new savings 37.5. Increase = 12.5 on 25 = 50%.
Explain it simply
Savings are what is left after spending, so they move by a different percentage from either income or spending. Because savings are a small slice, even a modest gap between how fast income and spending grow makes savings jump a lot. Pick income = 100 so every amount is also a percentage, and the arithmetic becomes simple.
Example
Question: Spending = 75% of income. Income rises 20%, spending rises 10%. Percentage change in savings?
| Income | Spending | Savings | |
|---|---|---|---|
| Before | 100 | 75 | 25 |
| After | 120 | 75 x 1.1 = 82.5 | 37.5 |
Increase in savings = 37.5 - 25 = 12.5. Percentage increase = 12.5 / 25 x 100 = 50%.
Check with real money: income ₹40,000, spending ₹30,000, savings ₹10,000. After: income ₹48,000, spending ₹33,000, savings ₹15,000, which is 50% more.
const before = 100 - 75;
const after = 120 - 75 * 1.1;
console.log(((after - before) / before) * 100); // Output: 50What to say in the interview
"I assume income is 100, so spending is 75 and savings 25. After the changes income is 120 and spending 82.5, so savings are 37.5. That is 12.5 more on a base of 25, a 50% rise."
Common mistakes
- Answering 10% (the difference of 20% and 10%).
- Applying the 20% income rise to savings directly.