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Speeds: 40, 60, 80

(1) Times 3:2:1 -> Total = 3a+2a+a = 6a

Distance: 40*3a+60*2a+80*a = 320a

Mean = 320a/6a = 320/6 = 160/3 km/h

Condition sufficient

(2) Distances 3:3:2 -> Total = 3a+3a+2a = 8a

Time: 3a/40+3a/60+2a/80 = 3a/40+a/20+a/40 = 6a/40 = 3a/20

Mean = 8a/(3a/20) = 160/3 km/h

Condition sufficient

Answer D
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Average speed total trip?

(1) Ratio of the times is 3:2:1, so times are 3i, 2i and i with i=integer

t = t1+t2+t3 = 3i+2i+i = 6i

l = l1+l2+l3 = 3i*40 + 2i*60 + i*80 = 320i

average speed = l/t = 320i/6i = 160/3

Condition (1) is sufficient

(2) Ratio of the lengths is 3:3:2, so lengths are 3i, 3i and 2i with i=integer

l = l1+l2+l3 = 3i+3i+2i = 8i

t = t1+t2+t3 = 3i/40 + 3i/60 + 2i/80 = 6i/40 = 3i/20

average speed = l/t = 8i/3i * 20 = 160/3

Condition (2) is sufficient

The answer is D
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(1) if ratio of times is 3:2:1 then times=3t+2t+t=6t

distances = 40*3t+60*2t+80t = 320t

Speed = 320t/6t = 160/3 km/h

Sufficient

(2) if ratio of distances is 3:3:2 then distances=3d+3d+2d=8d

times = 3d/40+3d/60+2d/80 = 3d/40+d/20+d/40 = 6d/40 = 3d/20

Speed = 8d/(3d/20) = 160/3 km/h

Sufficient

The correct answer is D
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3 legs of journey

First leg, avg speed = 40, distance = d1, time = t1
Second leg, avg speed = 60, distance = d2, time = t2
Third leg, avg speed = 80, distance = d3, time = t3

Total avg speed for trip = total distance/ total time = (d1+d2+d3)/(t1+t2+t3)

Statement A : t1:t2:t3 = 3:2:1 => t1 = 3x, t2 = 2x, t3 = x (let x be a constant)

D = S x T => d1 = 40x t1 = 60 x 3x = 120x
d2 = 60 x t2 = 60 x 2x = 120x
d3 = 80 x t3 = 80 x x = 80x

Avg speed = (120x + 120x +80x)/(3x+2x+x). X cancels out so avg speed can be calculated. Statement A alone is sufficient

Statement B : d1:d2:d3 = 3:3:2 =>d1 =3x, d2 =3x, d3 =2x (let x be a constant)

D = S x T = > T = D/S

T1 = d1/s1 = 3x / 40, similarly t2 = 3x / 60, t3 = 2x/80

Average speed = (d1+d2+d3)/(t1+t2+t3) = (3x+3x+2x)/(3x/40+3x/60+2x/80) X gets cancelled out and average speed can be calculated.

Statement B alone is sufficient

Each statement alone is sufficient. Answer D
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My ans is D)
We know the speeds at 3 legs, we need either the time or distance at each leg to find the average speed
1) Stat 1 gives ratio of time 3:2:1

For each leg assuming time taken as 3hr,2hr and 1 hr will give us the distance at each leg and thus the total distance. We have total distance and total time (6hrs)- SUFFICIENT

2) Stat 2 gives ratio of distance, assuming the distances as 300km, 300km and 200km we can find the time and total time- SUFFICIENT
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avg speed = total dist / total time

(1) time ratio = 3:2:1

take times as 3h, 2h, 1h.

dist = 40(3) + 60(2) + 80(1)

= 120 + 120 + 80 = 320

total time = 6h

avg speed = 320/6

can find exact ans.

suff

(2) dist ratio = 3:3:2

take dists as 3x, 3x, 2x.

time = 3x/40 + 3x/60 + 2x/80

total dist = 8x

so avg speed can also be found.

suff

each stmt alone is sufficient.

ans: d


Bunuel
A courier traveled from Hillford to Lakeshore in three consecutive legs, with no stops between the legs. On the first leg, the courier’s average (arithmetic mean) speed was 40 kilometers per hour; on the second leg, the courier’s average (arithmetic mean) speed was 60 kilometers per hour; and on the third leg, the courier’s average (arithmetic mean) speed was 80 kilometers per hour. What was the courier’s average speed for the entire trip?

(1) The ratio of the times the courier spent on the first, second, and third legs, respectively, was 3:2:1.

(2) The ratio of the lengths of the first, second, and third legs, respectively, was 3:3:2.


 


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In average speed formula, time are weights

(A) time ratio is given, we can derive average speed which is based on using time ratio as weights. Hence, Sufficient

(B) distance ratio is given and actual speeds too. Using D/S formula we can derive time ratio - similar reasoning as A from here. This is sufficient too.


(D) is the answer
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V(avg) = (d1+d2+d3)/(t1+t2+t3)

We know v1, v2, v3
We know V=d/t
Since we know V for each leg, to find out the d or t for each leg we need information on one or the other.

I) This gives us time information for each leg which means we can solve for distances of each leg. This means we have all we need to solve for the average.
SUFF.

II) This gives us distance information which can be used to solve for t of each leg.
SUFF.
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