SSC CGL 2023 PYQ — Question 51

The correct answer is option 4 i.e. $\frac{7}{55}$.

Let the initial amount of mixture be 80 litres.

Part of water = $80 \times {5\over 16}$ = 25 litres

Part of syrup = 80 - 25 = 55 litres

Let the mixture to be drawn be 16x.

According to the given question,

${{25 - 5x + 16x} \over {55 - 11x}} = {2 \over 3}$

⇒ ${{25 + 11x}\over {55 - 11x}} = {2\over 3}$

⇒ 75 + 33x = 110 - 22x

⇒ 55x = 35

⇒ x = $7 \over 11$

Now, 16x = $112 \over 11$

Also, the part of mixture to be drawn off = ${112 \over 11} \over 80$

⇒ $112 \over { 11 \times 80}$ = $7 \over 55$

Hence the required answer is $7 \over 55$.