Question : The time taken by boat to cover a distance of x km in upstream is 3 hours more than the time taken by the boat to cover the same distance in downstream. The speed of the boat in upstream is 8 km/hr. Which of the following statement(s) is/are correct?
I. If the value of x is 48 km, then the speed of the boat in downstream is 16 km/hr.
II. If the speed of the boat in downstream is 12 km/hr, then the value of x is 48 km.
Option 1: Neither I nor II
Option 2: Only II
Option 3: Only I
Option 4: Both I and II
Correct Answer: Only I
Solution :
Let the speed of the boat downstream as $d$ km/hr.
The time taken by the boat to cover $x$ km in downstream = $\frac{x}{d}$ hours
Upstream = $\frac{x}{8}$ hours
According to the question,
$\frac{x}{8} = \frac{x}{d} + 3$
Now check the statements:
I.
If $x = 48$ km
$\frac{48}{8} = \frac{48}{d} + 3$
$\therefore d = 16$ km/hr
So, statement I is correct.
II.
If $d = 12$ km/hr
$\frac{x}{8} = \frac{x}{12} + 3$
$\therefore x = 72$ km, not $48$ km
So, statement II is incorrect.
Hence, the correct answer is Only I.
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