A vessel contains a mixture of two liquids x and Y in the ratio 3 : 5. 8 litres of mixture are drawn off from the vessel and 8 litres of liquid x is filled in the vessel. If the ratio of liquids X and Y is now becomes 7: 10, how many litres of liquid X and Y were contained by the vessel initially ?
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : $X= 51\, lit, Y= 85 \, lit $
Let initially liquid X and Y be 3x lit and 5x lit respectively in the vessel.
After drawing off 8 lit of mixture
Quantity of liq X left in the mixture = $ 3x- \frac{3}{8}×8$
$= (3x-3)lit$
Quantity of liq Y left in the mixture $= 5x- \frac{5}{8} ×8$
$=(5x-5)lit$
So, quantity of liq X in the mixture $= (3x-3+8) lit$
$= (3x+5)lit$
Acc to given,
$\frac{7}{10}=\frac{3x+5}{5x-5}$
$35x-35=30x+50$
$5x= 85$
$x= 17 $
Hence, the quantity of liquid X = $3×17$
$= 51 lit $
The quantity of liq Y = $ 5×17$
$= 85 lit $