Ratio, Proportion and Variation

Question :- Two solutions, the first of which contains 0.8 kg and the second 0.6 kg of salt, were poured together and 10kg of a new salt solution were obtained.Find the weight of the first and of the second solution in the mixture if the first solution is known to contain 10% more of salt than the second.

(a) 4kg, 6kg
(b) 3kg, 7kg
(c) 4kg, 9kg
(d) 5kg, 9kg


Solution This Problem is very tricky.

let x be the quantity of 1st solution and y be the quantity of 2nd solution.
It is given that these solution are poured together to form 10kg of solution so we have 
=> x+y=10 ... eq1

Also the 1st solution contain 10% more salt than other
 => 0.8/x - 0.6/y = 10/100 ...eq2

Now here is the trap, after getting eq1 and eq2 DONT GO AHEAD TO SOLVE THE EQUATION. you'll end having too many quadratic equation and waste your time. instead use the given option.
option c and d are not possible as they don't add up to give 10. 
Out of option a and b only a fits the eq2.

 Answer : option a is correct.


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