M4maths Previous Puzzles

26 Mar 2014 Find the Speed

Vijay travels 600 km to his home party by train and partly by car. He takes 8 hours if he travels 120 km by train and rest by car. He takes 20 minutes longer if he travels 200 km by train and rest by car. Find the speed of the train.

OPtion

1) 70 km/hr
2) 75 km/h4
3) 65 km/hr
4) 85 km/h4
5) 50 km/hr
6) 80 km/hr
7) 60 km/hr
8) 55 km/hr
9) 90 km/hr
10)None of these

Solution

Le the speed of the train be x km/hr and speed of car be y km/hr
Vijay travels 120 km by train, the distance covered by car 600-120 = 480 km
Now, time taken to cover 120 km by train = 120/xhr
And time taken to cover 480 km by car = 480/y
Total time taken to travel 600 km = 120/x + 480/y = 8 hr (i)
Similarly
200/x + 400/y = 8hr. 20minute = 8(20/60) (ii)

solve (i) and (ii)
we get
x = 60 km/hr and y = 80 km/hr

Option 7) speed of train 60 km/hr

Correct Option: 7 Best Solution (36)

Akanksha Mishra   10 years AGO

Given
Total distance = 600 km
Consider speed of Train = x km/h
Consider speed of Car = y km/h
According to the question:
We know Time = distance/speed

Situation 1
He takes 8 hours if he travels 120 km by train and rest by car

120/x + 480/y = 8-------(1)

Situation (2)
when he travels 200 km by train and rest by car he takes 8 hr 20 min
8 hr 20 min = 25/3 hr

200/x + 400/y = 25/3 ---------(2)

solve equation 1 and 2

you'll get x = 60
so the speed of the train = 60 km/h(option 7)

Like? Yes (53) | No (18)  

Amit Kumar Panda   10 years AGO

If he goes by train more 80 km den the time increases 20 minute ..
if he goes less 80 km den ime decreases by 20 minute
120km bytrain+480km by car=8 hr
40km by train+560 km bycar=7hr 40 min
600 km bycar=7hr 30 min
car speed=80 km/hr
=>train speed =60 km/hr

Like? Yes (29) | No (7)  

Snehasis   10 years AGO

for 120 km it takes 8 hours and for each 80 kms 20 minutes is taken more then, in 10 hrs the train can travel full 600 kms. therefore, the speed of the train is 60km/h.

Like? Yes (26) | No (17)  

Ann Theressa   10 years AGO

Let x be the speed of train and y speed of car in km/hr.

Distance/speed = time taken

120/x + 480/y = 8 ---(1)

200/x + 400/y =25/3---(2)[time taken is 8hr 20min]

Multiply (1) by 5/4 and (2) by 3/2

150/x + 600/y = 10 ---(3)

300/x + 600/y = 25/2 ---(4)

equation (4) - (3)

150/x = 5/2
x = 150 * 2/5 = 60

Like? Yes (10) | No (4)  

Surya Narayana K   10 years AGO

Answer 60km/hr (Option 7).

Let speed of the train x and speed of the car y.

In first case,total duration is 8 hours(480 min) and train travels 120 km so 480=(120/x)+(480/y)
==>120y+480x=480 --(1)

similarly in the second case, total duration is 8 hr 20 min (500 min) and train travels 200 km .So 500=(200/x)+(400/y)==>200y+400x=500xy--(2)

After solving (1) and (2), we get 3y=4x --(3)

Substitute (3) in (1) , then x=60km/hr and y=80km/hr.

So train speed =60 km/hr (Option 7)

Like? Yes (8) | No (2)  

Nitin Jaiswal   10 years AGO

let the velocity of train be v1 and that of car be v2.
then,120/v1+480/v2=8
and 200/v1+400/v2=8.33
by solving the above 2 equations simultaneously we get v1(velocity of train)=60

Like? Yes (6) | No (2)  

S.SHAFI   10 years AGO

lets take speed of train be x km/h and speed of car be y km/h...
Equations will be

120/x + 480/y = 8 ---------(1)
200/x + 400/y = 25/3 ------(2) 8hr20min = 25/3hr

Solving these equations..

Speed of the train(x) = 60km/h
Speed of the car(y) = 80km/h..

Like? Yes (7) | No (4)  

Saidinesh   10 years AGO

120km by train. so remaining 480 by car. we can form an equation 120/x+480/y=8 eqn1 and if he travels 200km by train he took 20 mins extra. so 200/x+400/y=8hrs 20mins which is equal to 25/3 this is eqn no2. solve this both u can get value of x. x-speed of train& y-speed of car

Like? Yes (5) | No (2)  

AVIJIT   10 years AGO

let train's speed is and speed of car is y
1st equation is 120/x+480/y = 8.....(1)
and 2nd equation is 200/x+400/y = 25/3...(2)
8 hrs 20 min= 25/3 hrs
now solving two equation we will get x=60
train's speed is 60 km/hr

Like? Yes (4) | No (1)  

amit kumar   10 years AGO

120/x + 480/y =8
200/x + 400/y =8+20/60

2 equation and 2 unknown.solve for x and y

Like? Yes (5) | No (2)  

ARJYA HALDER   10 years AGO

Let, speed of the train be x &
speed of the bus be y.
From question (480/y)+(120/x)=8
& (400/y)+(200/x)=8+(1/3)

Solving these equations we get, x=60.

Like? Yes (4) | No (1)  

AKASH KUMAR   10 years AGO

Ans-7)60km/hr
equation:-
120/x + 480/y =8 (x=speed of train, y=speed of car)
from 2nd condition
200/x + 400/y =25/3 (a/q- 20 min more)
hence solving above 2 eq.
x=60km/hr
y=80km/hr.

Like? Yes (5) | No (2)  

Siddharth Singh   10 years AGO

let speed of train be t=1/x
and speed of car be c=1/y

when vijay travels 120 km by train and 480 by car,
the equation becomes:
=> 120/t +480/c = 8
=> 120x + 480y = 8

similarly, for second case
=> 200x + 400y= 25/3

solving the two equations,
=> 120x + 480y = 8
and
=> 200x + 400y= 25/3
we have x=1/60 and y=1/80

thus speed of train =>1/x = 60

Like? Yes (4) | No (1)  

muni   10 years AGO

consider speed of train is x and speed of car is y
total time equation if he travels on train 120km
120y+480x=8xy--1
total time equation if he travels on train 200km
200y+400x=25/3xy--2
solving 1 and 2 we get
x=60 and y=80

Like? Yes (3) | No (1)  

madanpal vishwakarma    10 years AGO

let assume that the speed of train is x and car is y
so according to the qustion
(120/x)+(480/y)=8h.......eq (i)
(200/x)+(400/y)=8h20minute

after solving this x=60 and y=80
so option 7 is corect

Like? Yes (3) | No (1)  

ANUP KUMAR   10 years AGO

We know that Time = Distance/speed
therefore there will be 2 eqn.
let x = speed of the train and y be the speed of car
1. 120/x + 480/y = 480 mins
2. 200/x + 400/y = 500 mins
by solving this 2 eqns we get x= 1 km/min = 60km/hr....
therefore speed of train is 60km/hr

Like? Yes (5) | No (3)  

SAM   10 years AGO

let speed of train = x km/hr
and speed of car = y km/hr
so,time taken by both in 1st case,

120/x + 480/y = 8......(1)
200/x + 400/y = 25/3......(2)

solve eqsn (1) & (2)

x=60km/hr
y=80km/hr

Like? Yes (5) | No (3)  

Vivek Jain   10 years AGO

120/Ts + 480/Cs = 8 ..(i)
200/Ts + 400/Cs = 25/3...(ii)
Ts=240/4=60Km/hr

Like? Yes (2) | No (1)  

Sudipta Mukherjee   10 years AGO

120/x+480/y=8
200/x+400/y=25/3
x=60km/hr

Like? Yes (2) | No (1)  

Suman Saurabh   10 years AGO

120/x + 480/y =8

200/x + 400/y = 25/3

so, x= 60km/hr

Like? Yes (2) | No (1)  

Rajasekhar Reddy   10 years AGO

120/T + 480/C = 8hr
200/T + 400/C = 8hr 20 min
solving above two equations
we get T = 60kmph

Like? Yes (4) | No (3)  

R.RAVIKUMAR   10 years AGO

Let the speeds of train and car be 'T' and 'C'..
From given instructions,

120/T + 480/C = 8hr
200/T + 400/C = 8hr.20min = 25/3 hr

By solving two equations,we get T = 60km/hr...

Like? Yes (4) | No (3)  

SIBNATH HALDER   10 years AGO

let train velocity=X,car velocity=Y
1st eq 120 X+480 Y=36000......(1)
2nd eq 200 X+400 Y=36020......(2)
after solve X=60.2 km/hr

Like? Yes (4) | No (3)  

saikiran   10 years AGO

480 minutes=(120/train velocity)+(480/car velocity)
500 minutes=(200/train velocity)+(400/car velocity)
by solving above euations
we get train vlocity=60km/hour

Like? Yes (3) | No (2)  

B karthik   10 years AGO

480 minutes=(120/train velocity)+(480/car velocity)
500 minutes=(200/train velocity)+(400/car velocity)
by solving above euations
we get train vlocity=60km/hour

Like? Yes (4) | No (3)  

Sofia Amreen   10 years AGO

et the speed of the train be x km/hr and that of the car be y km/hr.

Then, (120/x)+(480/y)= 8
(1/x)+(4/y)=1/15 ....(i)
And, (200/x) +(400/y)=25/3
(1/x)+(2/y)=1/24 ....(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.

Like? Yes (4) | No (3)  

Kumar   10 years AGO

as we know distance/speed=time
as we write the equations as per formula
we will get
120/x+480/y=8
200/x+400/y=25/3
solve above equations
for simplicity assume a=1/x,b=1/y;
then solve the equations
we will get x=60kmph,y=80kmph
finally train speed=60kmph

Like? Yes (4) | No (3)  

himesh suthar   10 years AGO

total km=600
by train 120
car=480
480/80=6
120/60=2
6+2=8 hours
now by train 200 km means it will take 200 min..
means 3 hours nd 20 min
nd remaining 400/80kmph=5
total =5 hours +3 hour nd 20 min.
so it took 20 min extra. so train speed 60kmph

Like? Yes (3) | No (2)  

BHAVNISH BHUTANI   10 years AGO

[(400*120)-(480*200)]/[(400*8)-(480*25/3)]=60

Like? Yes (2) | No (1)  

RAKESH   10 years AGO

120/x + 480/y = 8

200/x + 400/y = (8+ 1/3)

=> x=60

Like? Yes (2) | No (2)  

Devendra Marghade   10 years AGO

If Speed of train=x, car=y
1st Condition:(120/x)+(480/y)=8 ---(i) &
2nd Condition:(200/x)+(400/y)=[8+(1/3)] ---(ii)
Solving (i) & (ii), x=60, y=80

Like? Yes (2) | No (2)  

ASHISH MITTAL   10 years AGO

(120/t)+(480/c)=8
(200/t)+(400/c)=25/3
after solving we get t=60

Like? Yes (2) | No (2)  

ADVAITA BASAK   10 years AGO

60 km/hr

Like? Yes (2) | No (2)  

Rohit Agarwal   10 years AGO

let the speed of the train is vx and spped of car is vy.
so according to first condition

8=120/vx + 480/vy

so vx *vy=15*vy + 60*vx---------------(1)

and according to second condition

time=8+1/3=25/3

so 25/3=200/vx + 400/vy

so vx*vy=24*vy + 48*vx--------------(2)

by first and second condition

24*vy + 48*vx = 15*vy + 60*vx

so vy=4/3 * vx

putting vy in equation (1)

vx=60 km/hr

Like? Yes (3) | No (3)  

SONU GUPTA   10 years AGO

answer will be 60km/hr

Like? Yes (2) | No (2)  

Prerna   10 years AGO

120/t + 480/C= 8
200/t + 400/C= 25/3
solving these eqns, we get,
t=60 kmph

Like? Yes (2) | No (4)