Subject

    Quantitative Aptitude

    Topic

    Average

    One fourth of a journey is covered at the rate of 50 km/h, one third at the rate of 60 km/h and the rest at the rate of 100km/h. Find the average speed for the whole journey.

    ক)
    \(\;\frac{{1800}}{{63}}\;km/h\)
    খ)
    \(\;\frac{{1800}}{{53}}\;km/h\)
    গ)
    \(\frac{{3600}}{{53}}\;km/h\)
    ঘ)
    \(\;\frac{{360}}{{53}}\;km/h\)
    ঙ)
    None of these

    Explanation

    Let, the total distance travelled by train be ‘x’ km. ⇒ Time taken to travel one fourth part =x450=x200= \frac{{\frac{x}{4}}}{{50}} = \frac{x}{{200}} ⇒ Time taken to travel one third part =x/360=x180= \frac{{x/3}}{{60}} = \frac{x}{{180}} ⇒ Time taken to travel rest part (5/12) =5x12100=x240= \frac{{\frac{{5x}}{{12}}}}{{100}} = \frac{x}{{240}} ∴ Total time taken in the journey = 53  x  3600\frac{{53\;x\;}}{{3600}} Average speed of the whole journey = total distance/total time =x53x3600  =360053    km/h= \frac{x}{{\frac{{53x}}{{3600}}}}\; = \frac{{3600}}{{53}}\;\;{\rm{km}}/{\rm{h}}

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