Model 3 Problems on average speed Practice Questions Answers Test with Solutions & More Shortcuts
time & distance PRACTICE TEST [5 - EXERCISES]
Model 1 Basic Time & Distance using formula
Model 2 Vehicles in x/y of its usual speed
Model 3 Problems on average speed
Model 4 Time & Distance with Ratios
Model 5 Problems with Races
Question : 21 [SSC FCI Assistant Grade-III 2012]
One third of a certain journey is covered at the rate of 25 km/ hour, one-fourth at the rate of 30 km/hour and the rest at 50 km/ hour. The average speed for the whole journey is
a) 30 km/hour
b) 37$1/12$ km/hour
c) 35 km/hour
d) 33$1/3$ km/hour
Answer »Answer: (d)
Let the total distance be x km.
Total time = ${x/3}/25 + {x/4}/30 +{{5x}/12}/50$
= $x/75 + x/120 + x/120$
= $x/75 + x/60 = {4x + 5x}/300 = {3x}/100$ hours
Average speed
= $\text"Total distance"/\text"Time taken"$
= $x/{{3x}/100} = 100/3 = 33{1}/3$ kmph
Using Rule 18,If a man covers $1/x$ part of Journey at u km/h,$1/y$ part at v km/h and $1/z$ part at w km/hr and so on, then his average speed for the whole journey will be $1/{1/{xu} + 1/{yv} + 1/{zw} +...}$
Here, x = 3, u = 25
y = 4, v = 30
z = $12/5$ , w = 50
Average Speed= $1/{1/{xu} + 1/{yv} + 1/{zw}}$
= $1/{1/{3 × 25} + 1/{4 × 30} + 1/{12/5 × 50}}$
= $1/{1/75 + 1/120 + 1/120}$
= $1/{1/75 + 1/60} = 1/{{4 + 5}/300}$
= $300/9 = 100/3$
= 33$1/3$ km/hr.
Question : 22 [SSC CGL Tier-I 2016]
At an average of 80 km/hr Shatabdi Express reaches Ranchi from Kolkata in 7 hrs. The distance between Kolkata and Ranchi is
a) 560 m.
b) 650 m.
c) 560 km.
d) 506 km.
Answer »Answer: (c)
Distance = Speed × Time
= (80 × 7) km. = 560 km.
Question : 23 [SSC CGL Tier-I 2015]
A train runs at an average speed of 75 km/hr. If the distance to be covered is 1050 kms, how long will the train take to cover it ?
a) 15 hrs
b) 14 hrs
c) 13 hrs
d) 12 hrs
Answer »Answer: (b)
Using Rule 1,Distance = Speed × TimeSpeed = $\text"Distance"/\text"Time"$ , Time = $\text"Distance"/\text"Speed"$1 m/s = $18/5$ km/h, 1 km/h = $5/18$ m/s
Time = $\text"Distance"/\text"Speed"$
= $1050/75$ = 14 hours
Question : 24 [SSC CHSL 2014]
A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/ hr. His average speed for the whole journey in km/hr is
a) 35
b) 40
c) 37.5
d) 37
Answer »Answer: (c)
Using Rule 5,
Average speed of whole journey
= $({2xy}/{x + y})$ kmph
= ${2 × 50 × 30}/{50 + 30}$
= ${2 × 50 × 30}/80$ = 37.5 kmph
Question : 25 [SSC CPO SI 2016]
Durga walks 5 km from her home to school in 60 minutes, then bicycles back to home along the same route at 15 km per hour. Her sister Smriti makes the same round trip, but does so at half of Durga's average speed. How much time does Smriti spend on her round trip ?
a) 160 minutes
b) 80 minutes
c) 120 minutes
d) 40 minutes
Answer »Answer: (a)
Durga's average speed
= $({2xy}/{x + y})$ kmph.
= $({2 × 5 × 15}/{5 + 15})$ kmph.
= $({2 × 5 × 15}/20)$ kmph = $15/2$ kmph
Distance of School = 5 km.
Smriti's speed = $15/4$ kmph
∴ Required time = $2(5/{15/4})$ hours
= $({2 × 5 × 4}/15) = 8/3$ hours
= $(8/3 × 60)$ minutes = 160 minutes
IMPORTANT quantitative aptitude EXERCISES
Model 3 Problems on average speed Shortcuts »
Click to Read...Model 3 Problems on average speed Online Quiz
Click to Start..time & distance Shortcuts and Techniques with Examples
-
Model 1 Basic Time & Distance using formula
Defination & Shortcuts … -
Model 2 Vehicles in x/y of its usual speed
Defination & Shortcuts … -
Model 3 Problems on average speed
Defination & Shortcuts … -
Model 4 Time & Distance with Ratios
Defination & Shortcuts … -
Model 5 Problems with Races
Defination & Shortcuts …
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