Import Question JSON

Current Question (ID: 9677)

Question:

$\text{A swimmer swims a distance d upstream in 4 s and swims an equal distance downstream in 2 s. The ratio of swimmer's speed in still water to the speed of river water will be:}$

Options:

1. $\frac{6}{5}$
2. $\frac{3}{1}$
3. $\frac{5}{3}$
4. $\frac{4}{3}$

Solution:

$\text{Hint: Use the concept of relative velocity.}$ $\text{Step 1: Write the equation for upstream and downstream.}$ $\text{Let } v_M \text{ be the velocity of man in still water.}$ $\text{Let } v_W \text{ be the velocity of the river.}$ $\text{Let } d \text{ be the distance traveled.}$ $4 = \frac{d}{v_M - v_W}$ $2 = \frac{d}{v_M + v_W}$ $\text{Step 2: Find the ratio of velocities.}$ $\frac{(v_M + v_W) + (v_M - v_W)}{(v_M + v_W) - (v_M - v_W)} = \frac{2 + 1}{2 - 1}$ $\frac{v_M}{v_W} = \frac{3}{1}$ $\text{Hence, option (2) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}