# Questions tagged [ratio]

For questions concerning the ratio of a certain quantity to another.

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### Odds of winning a competition show with 10 contestants and 1 person eliminated each round

Say there are 10 contestants in a competition reality show. 1 contestant loses each episode and is removed from the show. Then in episode 2 there would be 9 contestants and so on with each episode. ...
34 views

### Divided Diamonds : a proportionality & ratio problem

Problem For stones of the same quality (e.g. the same colour), the monetary value of a diamond is proportional to the square of its mass (i.e. $C\propto M^2$). Find the monetary loss ($\Delta C$) ...
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### Constant area and ratio peculiarities regarding equilateral triangles.

I'm just writing this problem out of curiosity, so let me know whether I make any mistakes. FYI this problem was inspired by the 1998 AIME problem 12. Also, if you have a better name for this question,...
1 vote
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### relationship between proportions

consider some variables $x_1,x_2,y_1,y_2$ that are positive and for which $\frac{x_1}{y_1}=\frac{x_2}{y_2}=p$. Is it true that $\frac{x_1+x_2}{y_1+y_2}=p$?
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### Absolute Convergence of a Series (maybe use ratio test) [closed]

Let $p:=\lim_{{k \to \infty}} k(1-|\frac{a_{k+1}}{a_k}|)$ Prove $p>1$ or $p=\infty \implies \sum_{n=1}^\infty a_n$ converge absolutely
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### Is Basic Proportionality theorem applicable to trapezium? [closed]

I was studying vectors and came up with this question Show that the line joining the midpoints of two non parallel sides of a trapezium is parallel to the parallel sides and is equal to half of their ...
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### Turning division by zero to zero with basic math operators

I need to compute $\frac{const}{y}$, where $y$ may equal $0$ to present PC state in a human-readable format from exposed internal registers. Is it possible to build an expression of basic math ...
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### Contribution of a single value in a Division of Sums

I need to isolate contribution of a single entity in a Division of Sums as shown below. For example, find the contribution of variable a in the following: (a 1 + b ...
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### Determine point from one aspect ratio to an equivlent aspect ratio

I am working on a code program and get the X and Y coordinates of my cursor. My aspect ratio is 1280x720 and a point I am using for an example is (710, 300) however my x and y values must be 0.0-1.0, ...
43 views

### Converting a ratio into percentage.

As per many websites and text books, 3:4 converted into % is 75%. But as per my understanding, its not. If 3:4 is the ratio of boys and girls in a class, then it means that 3 out 7 are boys and 4 out ...
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### Ratio of two Jensen's Inequality

I have these pair of numbers $(a, b) = (\frac{4}{9}, \frac{1}{9})$ and $(c, d) = (\frac{1}{2}, \frac{1}{6})$. (Number mean nothing, just for illustration and simplification) Note that - (a, b) are ...
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### formula for reducing (as little as possible) one or both sides of a rectangle to match a given aspect ratio

I am writing a small program (for personal use). In the program, I need to be able to give a base ratio (such as 16:9), take a rectangle (such as 2048 x 1536), and reduce one or both sides of the ...
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### Algorithm for allocating whole gold bars amongst thieves by % share of the booty

I have N big gold bars and 1 small gold bar equivalent in weight to some fraction x of a large bar. E.g N = 10 and x = 0.5 then I have 10.5 large bars worth of gold, in 10 large bars and 1 small bar I ...
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1 vote
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### Compute the ratio : $\frac{\int_{0}^{\pi/2}\sin^{√2+1}xdx}{\int_{0}^{\pi/2}\sin^{√2-1}xdx}$ [duplicate]

I want to find the ratio of the following : $$\frac{\int_{0}^{\pi/2}\sin^{√2+1}xdx}{\int_{0}^{\pi/2}\sin^{√2-1}xdx}$$ I have tried a lot but can't solve it. Please help. Thanks.
27 views

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### Time and Work question - Case when people leave in between

Mr. X can do a job in 10 days, Mr. Y in 15 days and Mr. Z in 20 days. They work together for 2 days. Then Mr. X leaves the job. Mr. Y leaves the job a day earlier to the completion of the work. ...
132 views

### Dishonest shopkeeper at the time of buying as well as selling

James is a dishonest shopkeeper, and at the time of selling and purchasing, weighs 20% less and 10% more per kilogram respectively. Find the percentage profit earned by treachery. (Assume he sells ...
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### Confusion with the meaning of percentage higher, percentage increase

Question:- Had the rate of simple interest been higher by 2.5%, $£50,000$ would have amounted to $£82,750$ in 3 years. What did the sum of money amount to at the existing rate of interest ? I have ...
Question :- A shopkeeper claims he sells at 10% profit but his 1 kg weight actually measures 800 gram when selling and buying. Find his Profit/Loss % Author's solution :- $800 * 1000 * SP$ = \$(11/10) ...