Model 3 Problems on average speed Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on time & distance topic of quantitative aptitude
(a) $2/{x + y}$
(b) $1/x + 1/y$
(c) ${x + y}/{2xy}$
(d) ${2xy}/{x + y}$
The correct answers to the above question in:
Answer: (d)
Using Rule 5,
Required average speed = $({2xy}/{x + y})$ kmph
[Since, can be given as corollary If the distance between A and B be z units, then
Average speed = $\text"Totaldistance"/ \text"Time taken"$
= ${z + z}/{z/x + z/y}$
= $2/{1/x + 1/y} = 2/{{x + y}/{xy}} = {2xy}/{x + y}$
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Read more problems on average speed Based Quantitative Aptitude Questions and Answers
Question : 1
A man goes from Mysore to Bangalore at a uniform speed of 40 km/hr and comes back to Mysore at a uniform speed of 60 km/hr. His average speed for the whole journey is
a) 54 km/hr
b) 55 km/hr
c) 48 km/hr
d) 50 km/hr
Answer »Answer: (c)
Using Rule 5,
Average speed
= $({2xy}/{x + y})$ kmph
= $({2 × 40 × 60}/{40 + 60})$ kmph
= 48 kmph
Question : 2
A train goes from Ballygunge to Sealdah at an average speed of 20 km/hour and comes back at an average speed of 30 km/hour. The average speed of the train for the whole journey is
a) 25 km/hr
b) 24 km/hr
c) 27 km/hr
d) 26 km/hr
Answer »Answer: (b)
UsingRule 5,
Required average speed
= ${2 × 30 × 20}/{30 + 20}$
[Since, Distance covered is same]
= ${2 × 30 × 20}/50 = 24$ kmph
Question : 3
A constant distance from Chennai to Bangalore is covered by Express train at 100 km/hr. If it returns to the same distance at 80 km/hr, then the average speed during the whole journey is
a) 88.98 km/hr
b) 88.89 km/hr
c) 90.20 km/hr
d) 88.78 km/hr
Answer »Answer: (b)
Using Rule 5,
If same distance are covered at two different speed of x and y kmph,
the average speed of journey = ${2xy}/{x + y}$
= $({2 × 100 × 80}/{100 + 80})$ kmph
= 88.89 kmph
Question : 4
A man covers half of his journey at 6km/hr and the remaining half at 3km/hr. His average speed is
a) 4 km/hr
b) 3 km/hr
c) 9 km/hr
d) 4.5 km/hr
Answer »Answer: (a)
Using Rule 5,If a bus travels from A to B with the speed x km/h and returns from B to A with the speed y km/h,then the average speed will be $({2xy}/{x + y})$
If the same distance are covered at different speed of x kmph and y kmph,
the average speed of the whole journey is given by = $({2xy}/{x + y})$ kmph.
Required average speed
= ${2 × 6 × 3}/{6 + 3} = 36/9$ = 4 kmph
Question : 5
A boy rides his bicycle 10km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately :
a) 11.0 km/hr
b) 12.2 km/hr
c) 10.4 km/hr
d) 10.8 km/hr
Answer »Answer: (d)
Total distance = 10 + 12 = 22 km
Total time = $10/12 + 12/10 = 244/120$ hours
Required average speed
= $\text"Total distance"/ \text"Total time"$
= $22/{244/120} = 22/244 × 120$ = 10.8 km/hr.
Using Rule 3,If a man travels different distances $d_1,d_2,d_3$, and so on with different speeds $s_1,s_2,s_3$, respectively then,Average speed = $({d_1 + d_2 + d_3 + ...})/{d_1/S_1 + d_2/S_2 + d_3/S_3 + ...}$
Here, $d_1 = 10, S_1 = 12, d_2 = 12, S_2$ = 10
Average Speed = ${d_1 + d_2}/{d_1/S_1 + d_2/S_2}$
= ${10 + 12}/{10/12 + 12/10} = {22 × 120}/244$ = 10.8 km/hrs.
Question : 6
A man covers a total distance of 100 km on bicycle. For the first 2 hours, the speed was 20 km/ hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be
a) 15$1/8$ km/hr
b) 20 km/hr
c) 12$1/2$ km/hr
d) 13 km/hr
Answer »Answer: (c)
Distance covered in first 2 hours
= 2 × 20 = 40 km.
Remaining distance
= 100 - 40 = 60 km.
Time taken in covering 60 km at 10 kmph
= $60/10$ = 6 hours
∴ Required average speed
= $\text"Total distance"/ \text"Total Time"$
= $(100/{2+6})$ kmph = $(100/8)$ kmph
= $25/2$ kmph = 12$1/2$ kmph
GET time & distance PRACTICE TEST 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
time & distance Shortcuts and Techniques with Examples
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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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