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    Subject

    Quantitative Aptitude

    Topic

    Speed & Distance

    A boat can travel 24 km downstream in 4 hrs less time than it takes to travel the same distance upstream at a certain speed. If its speed is doubled and the speed of stream is tripled then it can travel 14/3 Km distance downstream in 1 hrs less time than it can upstream. Find the speed of stream.

    ক)
    20/3 kmph
    খ)
    10/3 kmph
    গ)
    8 kmph
    ঘ)
    16/3 kmph
    ঙ)
    4 kmph

    Explanation

    Let the stream's velocity be ‘x’ kmph Velocity of boat in still water = ‘s’ kmph From given conditions, 24(s−x)−24(s+x)=4  ⇒1s−x−1s+x=16\frac{{24}}{{\left( {s - x} \right)}} - \frac{{24}}{{\left( {s + x} \right)}} = 4\; \Rightarrow \frac{1}{{s - x}} - \frac{1}{{s + x}} = \frac{1}{6} s  +  x  −  s  +  x(s  −  x)(s  +  x)=16  12x=s2−x2  ........(i)\begin{array}{l} \frac{{s\; + \;x\;-\;s\; + \;x}}{{\left( {s\;-\;x} \right)\left( {s\; + \;x} \right)}} = \frac{1}{6}\;\\ 12x = {s^2}-{x^2}\; ........(i) \end{array} 14/3(2s−3x)−14/3(2s+3x)=1 ⇒12s−3x−12s+3x=314\frac{{14/3}}{{\left( {2s - 3x} \right)}} - \frac{{14/3}}{{\left( {2s + 3x} \right)}} = 1\ \Rightarrow\frac{{1}}{{2s - 3x}} - \frac{{1}}{{2s + 3x}} = \frac{3}{14} 2s+3x  −2s+3x(2s−3x)(2s+3x)=314  28x=4s2−9x2  .......(ii)\begin{array}{l} \frac{{2s + 3x\;-2s + 3x}}{{\left( {2s-3x} \right)\left( {2s+3x} \right)}}=\frac{3}{{14}}\;\\ 28x=4{s^2}-9{x^2}\;.......(ii) \end{array} Put x = (s2 - x2)/12 in equation.... (ii) and solve 7s 2 - 7x 2 = 12s 2 - 27x 2 20x 2 = 5s 2 4x 2 = s 2 Now put s 2 = 4x 2 in equation (i) and find the value of x 12x = 3x 2 x = 4 so speed of stream = 4kmph

    Related questions

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