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 ?

$X= 51\,  lit, Y= 85 \, lit $

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 $