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A man travels equal distances of his journey at 40, 30 and 15 km/h. respectively. Find his average speed for whole journey.

A. 24

B. 25

C. 27

D. 28

Answer: Option A

Solution(By Examveda Team)

Required average speed,
$$ = {\frac{{\left( {3 \times 40 \times 30 \times 15} \right)}}{{ {\left( {40 \times 30} \right) + \left( {40 \times 15} \right) + \left( {30 \times 15} \right)} }}} $$
$$ = 24\,{\text{km/hr}}$$

Alternatively
Time taken to traveled $$\frac{1}{3}$$ distance of journey with speed 40 kmph,
$$ = \frac{{ {\frac{1}{3}} }}{{40}} = \frac{1}{{120}}$$
Time taken to traveled $$\frac{1}{3}$$ distance of journey with speed 30 kmph,
$$ = \frac{{ {\frac{1}{3}} }}{{30}} = \frac{1}{{90}}$$
Time taken to traveled $$\frac{1}{3}$$ distance of journey with speed 15 kmph,
$$\eqalign{ & = \frac{{ {\frac{1}{3}} }}{{15}} = \frac{1}{{45}} \cr & {\text{Total time taken}} \cr & = {\frac{1}{{120}}} + {\frac{1}{{90}}} + {\frac{1}{{45}}} \cr & = \frac{{45}}{{1080}} \cr & {\text{Average speed}} \cr & = \frac{{{\text{Total distance traveled}}}}{{{\text{Total time taken}}}} \cr & = \frac{1}{{ {\frac{{45}}{{1080}}} }} \cr & = 24\,{\text{kmph}} \cr} $$

This Question Belongs to Arithmetic Ability >> Average

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Comments ( 7 )

  1. VEERESHA J
    VEERESHA J :
    3 years ago

    24 it is a wrong answer and 27 is the correct answer

  2. Ferdous Rahman
    Ferdous Rahman :
    6 years ago

    Let, Distance of one person 120(LCM of 40,30,15)
    1st Journy time taken by=120/40=3
    2nd.................................. =120/30=4
    3rd!.................................=120/15=8
    Average Speed=Total distance/Total Time
    =360/15=24
    Thanks

  3. Shiva Chanagani
    Shiva Chanagani :
    6 years ago

    avg distance formula= 3÷(1/x+1/y+1/z)
    now we have 1/40+1/30+1/15
    Lcm of 40,30,15 is 120
    then (3+4+8)/120=1/8
    from above formula 3÷1/8=3×8
    so ans=24

  4. Siddik Rahman
    Siddik Rahman :
    7 years ago

    Let ,Distance=x
    Since three separate speed completed the distance.
    So one part is x/3
    Now ,45km go by 1h
    1 " " " " "=1/45
    X/3 " =x×1/45×3=x/120
    At the same way....x/90,x/45.
    Total time taken=x/120+x/90+x/45=15x/360=x/24.
    So,average speed=Distance/Time=x/x/24=24.

  5. Kumar Chandan
    Kumar Chandan :
    8 years ago

    Time taken to traveled 1/3 distance of journey with speed 40 kmph,
    = (1/3)/40 = 1/120.
    Time taken to traveled 1/3 distance of journey with speed 30 kmph,
    = (1/3)/30 = 1/90.
    Time taken to traveled 1/3 distance of journey with speed 15 kmph,
    = (1/3)/15 = 1/45.
    Total time Taken = (1/120) + (1/90) + (1/45) = 45/1080.
    Average speed = Total distance traveled /total time taken = 1/(45/1080) = 24 kmph.

  6. Koti Reddy
    Koti Reddy :
    8 years ago

    i did not understand this question please give me the brief explaination

  7. Meg
    Meg :
    8 years ago

    but what is the formula used

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