Question

A trader mixes two varieties of coffee worth rs 160 per kg and 220 per kg and sells the mixture 189.20 per kg and makes a profit of 10%.In what proportion are the two varieties mixed.​

Answer 1

Let the variant worth 160 per kg be x kg. Then the other variant worth 220 per kg shall be (1-x)kg.

Since selling at 189.20 per kg yeilds 10% profit, the cost shall be = 189.20*100/110 i.e. 172 per kg.

Now the equation is,

x*160 + 220*(1-x) = 172

Solving this we get x= 0.8kg

So the variant mix is 0.8 kg of coffee worth 160 per kg and 0.2 kg of coffee worth 220 per kg for every kilogram of coffee sold by the merchant.

That gives the ratio of 4:1

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Answer 2

Answer:

Step-by-step explanation:

1. Let the quantity of 160 Rs. worth coffee in the mixture be $x$                        and  the quantity of 220 Rs. worth coffee in the mixture be $y$
2. The total mixture is one kg therefore,                                                                                                               $x+y =1$                  equation (1)
3. $y = (1-x)$
4. Selling price of the newly made mixture is 189.20 Rs. which is inclusive of 10% profit.
5. Therefore, Its cost price (CP) = 189.20 - 10% of CP.
6. CP = 189.20 - (189.20*$\frac{10}{110}$)
7. CP = 172 Rs.
8. Now, $160x + 220y = 172$         equation (2)
9. Putting the value of "y " from equation (1)    
10. We get, $160x + 220(1-x) = 172$
11. $160x + 220 - 220x = 172$
12. $x = 0.80kg$
13. Putting value of "y" in equation (1) we get $y= 0.20 kg$  
14. Hence two coffees are mixed in the ratio of  0.80: 0.20 .That is 4:1.    

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