# Word based problem with percentages

If your salary is increased by 10% and then after 6 months by a further 50%, what is the overall % increase?

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Here's a hint that always makes things easier for me -- Assume that your original salary is exactly $100. – Justin L. Dec 13 '10 at 9:07 ## 4 Answers Assume that in the question the further increase is based on the new salary and not the original one. Let the original salary be$x$. After the first increase, it becomes$\frac{110}{100}x$. After the second increase it becomes$\frac{150}{100}(\frac{110}{100}x)$. Hence the overall percentage increase from the original is$100(\frac{150}{100}(\frac{110}{100}x)-x)=65$. - But how do i find the overall % increase? – sammville Dec 12 '10 at 20:45 Sorry but it doesn't still answer my question. The answer is 65% but i am not sure how to get it. – sammville Dec 12 '10 at 21:03 NOTE:$\text{orig-salary}$represents the salary you had before it was changed.$\text{next-salary}$represents the salary you had after it was increased by 10%.$\text{final-salary}represents the salary you had after it was increased by 50%. Whenever we say "x was increased by y%" we mean this: $$x + (x * y\%) = (x * 100\%) + (x * y\%) = x * (100\% + y\%)$$ So, using the information in your problem, we have the following two equations: \begin{align*} \text{next-salary} &= \text{orig-salary} * (100\% + 10\%)\\ \text{final-salary} &= \text{next-salary} * (100\% + 50\%) \end{align*} Replace\text{next-salary}$with$\text{orig-salary} * (100\% + 10\%)\begin{align*} \text{final-salary} &= \text{next-salary} * (100\% + 50\%)\\ \text{final-salary} &= (\text{orig-salary} * (100\% + 10\%)) * (100\% + 50\%)\\ \text{final-salary} &= \text{orig-salary} * (110\%) * (150\%)\\ \text{final-salary} &= \text{orig-salary} * 1.10 * 1.50\\ \text{final-salary} &= \text{orig-salary} * 1.650 \end{align*} The overall increase would be1.650 - 100\%$OR$165.0\% - 100\% = 65\%$The overall increase is$65\%$. - If x is your original salary, 10 % increase in salary is obtained by multiplying 1.1 (since 0.1 is 10% of 1) Similarly 50 % increase in salary is obtained by multiplying 1.5 ( since 0.5 is 50% of 1) so with two consecutive increments of 10% and 50%. your new salary becomes 1.5 * (1.1*(x)) = 1.65*x. Work from here on... - I would like to suggest three quick formulas for tackling similar kind of problems: • If there is successive increase of$x\%$and$y\%$, then the net change will be $$x + y + \frac{x \cdot y}{100}\%$$ • If there is successive decrease of$x\%$and$y\%$, then the net change will be $$x + y - \frac{x \cdot y}{100}\%$$ • If there is$x\%$increase and then$y\%$decrease, then the net change is $$x - y - \frac{x \cdot y}{100}\%$$ Exercise: How does the last result change if there is$x\%$decrease followed by$y\%\$ increase?

These results can be easily verified, but it's always better to memorize them before any quantitative aptitude test.

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+1 You actually explained it all (at least, better than everyone else). :) –  muntoo Dec 14 '10 at 1:29