In a mixture of 240 cc, the ratio of the volumes of water and glycerine is 1: 3. The quantity of water (in cc) that should be added to the mixture, so that the new ratio of the volumes of water and glycerine becomes 2 : 3, is [SSC (CGL) 2014] |
A) 55 cc
B) 60 cc
C) 62.5 cc
D) 64 cc
Correct Answer: B
Solution :
(b) Given, total mixture \[=240\,\,cc\] |
Ratio of water and glycerin \[=1:3\] |
Let the quantity of water be x |
and quantity of glycerin \[=3x\] |
Then, \[x+3x=240\] |
\[\Rightarrow \] \[4x=240\] \[\Rightarrow \] \[x=60\] |
\[\therefore \]Quantity of water \[=60\,\,cc\] |
and quantity of glycerin \[=3x=3\times 60=180\,cc\] |
Now, according to the question, |
New ratio of water and glycerin \[=2:3\] |
Let x (cc) of water be added to make the required ratio. |
Then, \[\frac{60+x}{180}=\frac{2}{3}\] |
\[\Rightarrow \]\[180+3x=360\]\[\Rightarrow \]\[3x=180\] |
\[\Rightarrow \]\[x=\frac{180}{3}\]\[\Rightarrow \]\[x=60\,cc\] |
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