SSC Sample Paper SSC CGL - Sample Paper-2

  • question_answer
    Several litres of acid were drawn off a 54 L vessel full of acid and an equal amount of water added. Again the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 L of pure acid. How much of the acid was drawn off initially?

    A)  12 L                            

    B)  16 L     

    C)  18 L                

    D)  24 L

    Correct Answer: C

    Solution :

    Let x L of several litres of acid drawn off initially. \[\therefore \] Remaining acid in the vessel             \[=(54-x)L\] And quantity of water in the vessel \[=x\,L\] Now x L mixture is drawn off. \[\therefore \] Quantity of acid drawn off             \[=\left( \frac{54-x}{54}\times x \right)L\] And quantity of water drawn off \[=\frac{{{x}^{2}}}{54}L\] Now the quantity of acid \[=\left[ 54-x-\left( \frac{54-x}{54} \right)x \right]L\] \[\therefore \]      \[54-x-\frac{(54-x)}{54}x=24\] \[\Rightarrow \]   \[{{x}^{2}}-108x+1620=0\] \[\Rightarrow \]   \[x=90,\,\,18\] Since 90 > 54 there x = 90 is ruled out Hence,              x = 18 

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