Model 2 Vehicles in x/y of its usual 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 : 6 [SSC CGL Prelim 2005]
Walking at three-fourth of his usual speed, a man covers a certain distance in 2 hours more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is
a) 5 hours
b) 6 hours
c) 5.5 hours
d) 4.5 hours
Answer »Answer: (b)
$4/3$ × usual time - usual time = 2
$1/3$ usual time = 2
Usual time = 2 × 3 = 6 hours
Using Rule 8,
Here, $\text"A"/ \text"B"= 3/4$, time= 2 hrs.
Usual Speed
= $\text"A"/\text"Diff of A and B"$ × time
= $3/{(4 - 3)} × 2$ = 6 hours
Question : 7 [SSC GL Tier-I 2013]
By walking at $3/4$ of his usual speed, a man reaches his office 20 minutes later than his usual time. The usual time taken by him to reach his office is
a) 30 minutes
b) 40 minutes
c) 60 minutes
d) 75 minutes
Answer »Answer: (c)
$4/3$ of usual time
= Usual time + 20 minutes
$1/3$ of usual time = 20 minutes
Usual time = 20 × 3 = 60 minutes
Using Rule 8,
Here, A = 3, B= 4, t = 20 minutes
Usual time taken
= $\text"A"/\text"Diff of A and B"$ × time
= $3/{(4 - 3)} × 20$ = 60 minutes
Question : 8 [SSC CGL Tier-1 2011]
Walking at $6/7$th of his usual speed a man is 25 minutes late. His usual time to cover this distance is
a) 2 hours 10 minutes
b) 2 hours 25 minutes
c) 2 hours 15 minutes
d) 2 hours 30 minutes
Answer »Answer: (d)
Time and speed are inversely proportional.
$7/6$ × Usual time - Usual time = 25 minutes
Usual time $(7/6 -1)$
= 25 minutes
Usual time × $1/6$
= 25 minutes
Usual time = 25 × 6
= 150 minutes
= 2 hours 30 minutes
Using Rule 8,
Here, A = 6, B = 7, t = $25/60 = 5/12$ hrs.
Usual time = $\text"A"/\text"Diff of A and B"$ × time
= $6/{(7 - 6)} × 5/12 = 5/2$ hrs.
= 2 hours 30 minutes
Question : 9 [SSC CGL Prelim 2005]
A train running at $7/11$ of its own speed reached a place in 22 hours. How much time could be saved if the train would run at its own speed?
a) 16 hours
b) 8 hours
c) 7 hours
d) 14 hours
Answer »Answer: (b)
Since the train runs at $7/11$ of its own speed,
the time it takes is $11/7$ of its usual speed.
Let the usual time taken be t hours.
Then we can write, $11/7$ t = 22
t = ${22 × 7}/11$ = 14 hours
Hence, time saved
= 22 - 14 = 8 hours
Question : 10 [SSC CGL Tier-I 2014]
A car travels from P to Q at a constant speed. If its speed were increased by 10 km/h, it would have been taken one hour lesser to cover the distance. It would have taken further 45 minutes lesser if the speed was further increased by 10 km/h. The distance between the two cities is
a) 620 km
b) 600 km
c) 420 km
d) 540 km
Answer »Answer: (c)
Fixed distance = x km and certain speed = y kmph (let).
Case I,
$x/{y +10} = x/y$ - 1
$x/{y +10} + 1 = x/y$ --- (i)
Case II,
$x/{y + 20} = x/y - 1 - 3/4$
= $x/y - {4 + 3}/4$
$x/{y + 20} + 7/4 = x/y$ --- (ii)
From equations (i) and (ii),
$x/{y +10} + 1 = x/{y + 20} + 7/4$
$x/{y +10} - x/{y + 20} = 7/4$ - 1
$x({y + 20 - y - 10}/{(y + 10)(y + 20)})$
= ${7 - 4}/4 = 3/4$
${x × 10}/{(y + 10)(y + 20)} = 3/4$
3 (y + 10) (y + 20) = 40 x
${3(y + 10)(y + 20)}/40$ = x --(iii)
From equation (i),
${3(y + 10)(y + 20)}/{40(y + 10)}$ + 1
= ${3(y + 10)(y + 20)}/{40y}$
3 (y +20) + 40 = ${3(y + 10)(y + 20)}/y$
$3y^2 + 60y + 40y$
= $3(y^2 + 30y + 200)$
$3y^2 + 100y = 3y^2 + 90y + 600$
10y = 600 ⇒ y = 60
Again from equation (i),
$x/{y +10} + 1 = x/y$
$x/{60 + 10} + 1 = x/60$
$x/70 + 1 = x/60$
${x + 70}/70 = x/60$
6x + 420 = 7x
7x - 6x = 420
$x$ = 420 km.
IMPORTANT quantitative aptitude EXERCISES
Model 2 Vehicles in x/y of its usual speed Shortcuts »
Click to Read...Model 2 Vehicles in x/y of its usual 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 …
quantitative aptitude CATEGORIES
RECENT BLOGS
Recently Added Subject & Categories For All Competitive Exams
Ratio and Proportion Questions with Solutions, IBPS Clerk
New Ratio and Proportion Quants Aptitude based Multiple Choice Questions and Answers Practice Test Series, Quiz & Mock Test for IBPS Clerk Prelims 2024 Exam
Continue Reading »
Top Analogy Reasoning Ability For IBPS Clerk Prelims 2024
Most Important Analogy based Verbal Reasoning Multiple choice questions and answers practice quiz series PDF, Free New Mock tests For IBPS Clerk Prelims 2024
Continue Reading »
SSC STENO: Mensuration Area & Volume Questions Test PDF
Free Mensuration Area and Volume Aptitude-based Practice multiple questions with solutions, Quiz, Full Mock Test & PDF for SSC Steno (Grade C & D) 2024 Exam
Continue Reading »
SSC STENO: Speed Time and Distance MCQ Questions Test PDF
Free Time and Distance Aptitude-based Practice multiple questions with solutions, Quiz series, Mock Test & Download PDF for SSC Steno (Grade C & D) 2024 Exam
Continue Reading »