Model 5 Problems with Races 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 : 11 [SSC CGL Tier-I 2015]
Walking at the rate of 4 kmph a man covers certain distance in 2 hrs 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in how many minutes ?
a) 35 min.
b) 45 min.
c) 40 min.
d) 50 min.
Answer »Answer: (c)
2 hours 45 minutes
= $(2 + 45/60)$ hours
= $(2 + 3/4)$ hours = $11/4$ hours
Distance = Speed × Time
= 4 × $11/4$ = 11 km.
Time taken in covering 11 km at 16.5 kmph
= $11/{16.5}$ hour
= $({11 × 10 × 60}/165)$ minutes
= 40 minutes
Question : 12 [SSC CPO S.I.2007]
In a race of 200 metres, B can give a start of 10 metres to A, and C can give a start of 20 metres to B. The start that C can give to A, in the same race, is
a) 25 metres
b) 27 metres
c) 29 metres
d) 30 metres
Answer »Answer: (c)
According to the question,
Since, When B runs 200 m metres, A runs 190 metres
When B runs 180 metres, A runs
= $190/200 × 180$ = 171 metres
When C runs 200m, B runs 180 metres.
Hence, C will give a start to A by
= 200 - 171 = 29 metres
Question : 13 [SSC CPO S.I.2007]
In a race of 800 metres, A can beat B by 40 metres. In a race of 500 metres, B can beat C by 5 metres. In a race of 200 metres, A will beat C by
a) 1.19 metre
b) 1.27 metre
c) 12.7 metre
d) 11.9 metre
Answer »Answer: (d)
According to the question,
When A runs 800 metres, B runs 760 metres
When A runs 200 metres, B runs
= $760/800 × 200$ = 190 metres
Again, when B runs 500 metres, C runs 495 metres.
When B runs 190 metres, C runs
= $495/500 × 190$ = 188.1 metres
∴ Hence, A will beat C by
200 - 188.1 = 11.9 metres in a race of 200 metres.
Question : 14 [SSC SO 2006]
In a one-kilometre race A, B and C are the three participants. A can give B a start of 50 m. and C a start of 69 m. The start, which B can allow C is
a) 20 m.
b) 18 m.
c) 19 m.
d) 17 m.
Answer »Answer: (a)
Let the time taken to complete the race by A,B, and C be x minutes.
Speed of A = $1000/x$,
B = ${1000 - 50}/x = 950/x$
C = ${1000 - 69}/x = 931/x$
Now, time taken to complete the race by
B = $1000/{950/x} = {1000 × x}/950$
and distance travelled by C in
${1000x}/950$ min = ${1000x}/950 × 931/x$ = 980 km.
B can allow C
= 1000 - 980 = 20 m
Question : 15 [SSC CPO S.I.2008]
In a race of one kilometre, A gives B a start of 100 metres and still wins by 20 seconds. But if A gives B a start of 25 seconds, B wins by 50 metres. The time taken by A to run one kilometre is
a) $500/29$ seconds
b) $700/29$ seconds
c) $1200/29$ seconds
d) 17 seconds
Answer »Answer: (a)
Let A take x seconds in covering 1000m and b takes y seconds
According to the question,
x + 20 = $900/1000$ y
x + 20 = ${9y}/10$ ...(i)
and, $950/1000$ x + 25 = y ...(ii)
From equation (i),
${10x}/9 + 200/9 = y$
${10x}/9 + 200/9 = {950x}/1000 + 25$
${10x}/9 + 200/9 = {19x}/20 + 25$
${10x}/9 - {19x}/20 = 25 - 200/9$
${200x - 171x}/180 = {225 - 200}/9$
${29x}/180 = 25/9$
$x = 25/9 × 180/29 = 500/29$ seconds.
IMPORTANT quantitative aptitude EXERCISES
Model 5 Problems with Races Shortcuts »
Click to Read...Model 5 Problems with Races 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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