Latest CTS Aptitude Question SOLUTION: A man covers a distance of 1200 km in 70 days resting 9 hours a day, if he rests 10 hours a day and walks with speed 1½ times of the previous in how many days will he cover 750 km

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A man covers a distance of 1200 km in 70 days resting 9 hours a day, if he rests 10 hours a day and walks with speed 1½
times of the previous in how many days will he cover 750 km?

1: 30
2: 31.25
3: 31
4: 33

Asked In CTS Minakshi Kumari (10 years ago)

Solved Saraswathy Read Solution (11)

Is this Puzzle helpful?   (74)   (15) Submit Your Solution Time Distance and Speed

Read Solution (11) :

Saraswathy  (10 years ago)

Distance d = 1200km
let x be the speed

he walks 15 hours a day(ie 24 - 9)... so totally he walks for 1050hrs...

x = 1200/1050 => 120/105 = 24/21 => 8/7kmph


given 1 1/2 of prev speed
so 3/2 * 8/7= 24/14 = 12/7

new speed = 12/7kmph

now he rests 10 hrs a day ... means he walks 14 hrs a day...

time = 750 * 7 /12 => 437.5hrs
=> 437.5/14 = 31.25

so he ll take 31.25 days to cover 750km

Is this solution Helpfull? Yes (162) | No (1)  

Trishul  (10 years ago)

31.25 (Answer)


Case 1:
Total Distance = 1200km
Total time=70*(24-9)=1050
Speed=D/T=1200/1050

Case 2:
Speed = (old speed*1.5)= (1200/1050)*1.5
Distance = 750
Time = Dis/Speed = 750/((1200/1050)*1.5)=437.5
Now resting 10 hrs a day ie. working 14 hrs a day
therfore 437.5/14=31.25 (Answer)

Is this solution Helpfull? Yes (22) | No (1)  

Saraswathy  (10 years ago)

2) 31.25 days

Is this solution Helpfull? Yes (5) | No   

mb  (10 years ago)

2)31.25

70 days---1200km
1day= 1200/70= 120/7
1day=24 hrs he rests 9 hrs a day so, left hrs= 15hrs
speed=distance/time
x={120/7}/ 15
x=8/7km/hr
if he rests 10 hrs a day and walks with speed=3/2x
then he walks for 14 hrs a day
again 3/2x= 750/ 14
putting value of x=8/7
14hrs/day= 750*7*2/3*8
14hrs/day= 437.5
1 day= 437.5/14 =31.25

Is this solution Helpfull? Yes (5) | No   

anjan  (9 years ago)

(d2*t2*v2)/s2=(d1*t1*v1)/s1
d2=70*15*1*750/(1200*3/2*14)
=31.25

Is this solution Helpfull? Yes (4) | No   

kalprajanand  (10 years ago)

since he rest 10 hrs a day so he travels 14 hrs in a day at speed of 3/2 so his in one day he walks 21 km so 750 km he will walk in 33 days

Is this solution Helpfull? Yes (1) | No (4)  

Yogesh  (10 years ago)

big in size

Is this solution Helpfull? Yes (1) | No   

Sai Krishna  (8 years ago)

we know that Distance= Speed*time,
here D=1200km;
total journey per day = 24-9=15 hours,
i.e, for 70 days is 70*15= 1050 hrs
now Speed = distance/time
speed = 1200/1050 =1.14 km/hr

now the new speed is 1.5 times of the old speed
i.e., 1.5*1.14= 1.71
he take rest for 10 hours a day i.e., he travels 14 hours per day

total time =750/(1.71*14) = 31.258
therefore number of days for walking 750 km takem by him is 31.25

Is this solution Helpfull? Yes (1) | No   

Ayush Sood  (10 years ago)

31.25 days

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rakesh chunduru  (7 years ago)

you can apply MANDAYS concept ,
let x days to cover 750km
man*days*hours+w2=man*days*hours*w1
70*15*750=1200*(x)*14*1.5*1200(speed for 1200km is y and speed for 750km is 3/2(y))
which gives x=31.5

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shweta kumari  (7 years ago)

31.25 days

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