DSSSB TGT CS 2023 Shift 2 – Question 054

The time taken by a boat to go 21 km downstream is equal to the time taken by it to go 9 km upstream. To go 12 km downstream and the same distance upstream, it takes a total of \(5\frac{5}{7}\text{ hours}\). How much time (in hours) will the boat take to go 28 km downstream?

• \(3\frac{1}{9}\)
• \(3\frac{1}{2}\)
• 4
• 5

Step 1: Set up the relation between downstream and upstream speeds:
Let downstream speed be \(D\) and upstream speed be \(U\).
Given that time taken for 21 km downstream equals time taken for 9 km upstream:
\[ \frac{21}{D} = \frac{9}{U} \implies \frac{D}{U} = \frac{21}{9} = \frac{7}{3} \]
Let \(D = 7k\) and \(U = 3k\).

Step 2: Use the total time equation:
Total time taken to go 12 km downstream and 12 km upstream is \(5\frac{5}{7} = \frac{40}{7}\) hours:
\[ \frac{12}{D} + \frac{12}{U} = \frac{40}{7} \]
\[ \frac{12}{7k} + \frac{12}{3k} = \frac{40}{7} \]
\[ \frac{12}{k} \left( \frac{1}{7} + \frac{1}{3} \right) = \frac{40}{7} \]
\[ \frac{12}{k} \times \frac{10}{21} = \frac{40}{7} \]
\[ \frac{120}{21k} = \frac{40}{7} \implies \frac{40}{7k} = \frac{40}{7} \implies k = 1 \]

Step 3: Find downstream speed \(D\):
\[ D = 7k = 7 \times 1 = 7\text{ km/h} \]

Step 4: Calculate time taken to go 28 km downstream:
\[ \text{Time} = \frac{\text{Distance}}{D} = \frac{28}{7} = 4\text{ hours} \]
Hence, the correct answer is option c).