calculate ratios of two rice

Question

Joseph bought two varieties of rice, costing $5$ cents per ounce and $6$ cents per ounce each, and mixed them in some ratio. Then he sold the mixture at $7$ cents per ounce, making a profit of 20 percent. What was the ratio of the mixture?

my approaches is following,first of all if we have income and cost,profit percent is

$(income-cost)*100/(cost)$

let us denoted rice with $5$ cent per ounce by $x$ and second by $y$,total cost is $5*x+6*y$

income is $7*(x+y)$,profit we have $2*x+y$,so percentage we have

$(2*x+y)/(5*x+6*y)=0.2$

after calculation we have $x/y=0.2=1/5$

is my approaches correct?

amWhy · Accepted Answer · 2013-08-10T20:05:02.480

3

$$\begin{align} \dfrac{(2x+y)}{(5x+6y)} & =0.2 \\ \\ 2x + y & = 0.2(5x + 6y) \\ \\ x &= 1.2y - y = .2 y \\ \\ \dfrac xy &= .2 = \frac 15\end{align}$$

So yes, the correct ratio is $$x:y = 1 \text{part 5-cent rice}:5 \text{parts 6-cent rice}$$

edited Aug 10 '13 at 20:05

answered Aug 10 '13 at 19:57

amWhy

209,954

sorry 3.2?why it is so? – dato datuashvili Aug 10 '13 at 19:58
no no 6*0.2=1.2 – dato datuashvili Aug 10 '13 at 20:00
that is GRE difficult problem – dato datuashvili Aug 10 '13 at 20:06
@amWhy: made me hungry! :-) +1 – Amzoti Aug 11 '13 at 08:11
Why Amzoti? What made you hungry? +) – Mikasa Aug 13 '13 at 09:26

DJohnM · Answer 2 · 2013-08-10T20:58:10.847

For a hand waving solution:

a $7$ cent price gives a $20\%$ profit, so it must be $120\%$ of cost. So cost is:$$7\times \frac{100}{120}=7 \times\frac{5}{6}=\frac{35}{6}=5\frac{5}{6}$$So, you're $\frac{5}{6}$th of your way from the cheap rice cost to the expensive rice cost, so you must be $\frac{5}{6}$th of your way from pure cheap to pure expensive in the mix. So $20\%$ cheap and $80\%$ expensive.

Ooops! I should have said $5:1$ expensive to cheap...

calculate ratios of two rice

2 Answers2