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One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.
Answer & Solution
Correct Answer:
Option
C
Let distance be 120 km
Hence 30 km is covered by @25 kmph and 40 km covered by @30 kmph and rest 50 km has been covered @50 kmph
Now,
$$\eqalign{ & {\text{average}} = {\frac{{120}}{{{\text{total}}\,{\text{time}}\,{\text{taken}}}}} \cr & = \frac{{120}}{{\frac{{30}}{{25}} + \frac{{40}}{{30}} + \frac{{50}}{{50}}}} \cr & = \frac{{3600}}{{106}} \cr & = \frac{{1800}}{{53}}\,{\text{km/h}} \cr} $$
Now,
$$\eqalign{ & {\text{average}} = {\frac{{120}}{{{\text{total}}\,{\text{time}}\,{\text{taken}}}}} \cr & = \frac{{120}}{{\frac{{30}}{{25}} + \frac{{40}}{{30}} + \frac{{50}}{{50}}}} \cr & = \frac{{3600}}{{106}} \cr & = \frac{{1800}}{{53}}\,{\text{km/h}} \cr} $$
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LoginB = 1/3 of the distance x
C = the rest distance
if the whole distance is X then the sum of 1x/4, 1x/3 and the rest distance is equal
x= 1x/4 + 1x/3 + rest
rest = x-1x/12
rest = 5x/12
average velocity = (distance total)/total time taken
= x/x(1/100 + 1/90 + 5/600)
= 1/[564/5400]
Remaining 1-(7/12)=50
5x/12=50
X=120
x/4/25 +x/3/30 + 5x/12/50(where 12=4*3)
then:
we get, x/100+x/90+x/120
=18x+20x+15x/1800
+53x/1800
so,to find average speed for whole journey is,
x/53x/1800
=1800x/53x
=1800/53
30+25+40+90=120
So you take a number which will be divisible by 3 , 4 and 1 .
Which is 12
And we need it in Kms so we take 120 instead