DSSSB TGT CS 2023 Shift 2 – Question 044

The ratio of spirit and water in solution A is \(6 : 7\) and the ratio of water and spirit in solution B is \(9 : 4\). 3 L of A is mixed with 5 L of B. In 780 mL of the resulting solution, what is the quantity (in mL) of spirit?

• 285
• 304
• 270
• 266

Step 1: Determine the fraction of spirit in each solution:
In solution A:
Ratio of spirit to water = \(6 : 7\)
\[ \text{Fraction of spirit in A} = \frac{6}{6 + 7} = \frac{6}{13} \]

In solution B:
Ratio of water to spirit = \(9 : 4\) (Note: spirit is the second term!)
\[ \text{Fraction of spirit in B} = \frac{4}{9 + 4} = \frac{4}{13} \]

Step 2: Find total spirit in the mixture of 3 L of A and 5 L of B:
Total volume = \(3 + 5 = 8\text{ L}\)
\[ \text{Spirit from A} = 3 \times \frac{6}{13} = \frac{18}{13}\text{ L} \]
\[ \text{Spirit from B} = 5 \times \frac{4}{13} = \frac{20}{13}\text{ L} \]
\[ \text{Total spirit in mixture} = \frac{18}{13} + \frac{20}{13} = \frac{38}{13}\text{ L} \]

Step 3: Find fraction of spirit in the mixture:
\[ \text{Fraction of spirit} = \frac{\frac{38}{13}}{8} = \frac{38}{104} = \frac{19}{52} \]

Step 4: Calculate the volume of spirit in 780 mL of the resulting solution:
\[ \text{Quantity of spirit} = 780 \times \frac{19}{52} = 15 \times 19 = 285\text{ mL} \]
Hence, the correct answer is option a).