Latest Elitmus Aptitude Question SOLUTION: abhishek started from Bangalore to kysore and aishwarya from opposite direction. They met at a resturant mid way and had lunch for 30 minutes. Abhishek travelled 180 km more than a

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(#M40030589) ELITMUS Numerical Ability question Keep an EYE

abhishek started from Bangalore to kysore and aishwarya from opposite direction. They met at a resturant mid way and had lunch for 30 minutes. Abhishek travelled 180 km more than aishwarya. After they departed abhishek took 2 hrs to reach kysore and aishwarya 4.5 hours. If they traveled with uniform speed. wat will be the distance between two cities?

Asked In Elitmus Harshvardhan Nilmani (11 years ago)

Unsolved Read Solution (20)

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Saatvika Dhumeja  (10 years ago)

let aishwarya travels x km in order to meet abhishek with speed bkm/hr,
abhishek travelled 180km more, i.e distance travelled by abhishek= x+180, with speed a km/hr.

time(abhi)=time(aish)
x/b=(x+180)/a -----(1)

now,the 2nd condition i.e after lunch-
distance that aish has to travel is x+180km and time taken by her is 4.5hr
abhi has to travel x km and in 2hrs
so,

2=x/a i.e
a=x/2

and 4.5=(x+180)/b
b=(x+180)/4.5

substitute these values of a and b in equation (1)

4.5x/(x+180) = 2(x+180)/x on solving we get x=360.

so total distance is x+x+180=900

Is this solution Helpfull? Yes (25) | No (1)  

K.ARun  (11 years ago)

Total hr=2+4.5=> 6.5 hrs.
so, if they both travelled at 70km/hr means then abishek travelled dist=315 and aish travelled distance=140.
but 315-140=175 dist abishek travelled more..(condition is 180)..
so now take 71km/hr, so abi travelled =319.5 and aish travelled=142
their diff. is 177.5..
now take 72km/hr abi travelled=324 and aish travelled=144
and abishek hv travelled 180 km more than aishwarya now...
so total distance = 144+324... so 468

Is this solution Helpfull? Yes (20) | No (11)  

alok chand  (11 years ago)

x^2-288x-25920=0
from this equation x=360.
and total distance coverd by abhishek is {(180+x)till restro}+{(x)from restro to kysore}.
so 180+x+x=180+2x.
tatal distance=180+2*360=900.

Is this solution Helpfull? Yes (8) | No (2)  

Harshvardhan Nilmani  (11 years ago)

let speed of abhishek is a and of aishwarya is b
Distance traveled by aishwarya till restaurant be x
So distance traveled by abhishek is x+180
Time(abhishek)=Time (aishwarya) /*till restaurant*/
so x+180/a = x/b;
also, after passing restaurant
for abhishek a= x/2 ;
and for aishwarya b = x+180/4.5;
three equations will result to
2x+360/x = 4.5x/x+180
solving this result will be eqn 2.5x*x -720x -64800 = 0;
how to get answer after this..
options are
1) 720
2) 540
3) 480
4) 360

Is this solution Helpfull? Yes (7) | No (4)  

Suman Bhowmick  (10 years ago)

Let, distance traveled by aishwarya = x km
distance traveled by abhishek = (x+180) km

to reach aishwarya's initial location, abhishek travels x km in 2 hrs. and
aishwarya travels (x+180) km in 4.5 hrs to reach abhishek's initial position.

Given, Abhishek's speed = Aishwarya's speed
x/2=(x+180)/4.5
x=144

So total distance = x + (x+180)= 468 km

Is this solution Helpfull? Yes (7) | No (4)  

mohan lal garg  (11 years ago)

ans is 900
abhishekmeeet point
abhishek speed =180 km/hr
aishwarya speed =120 km.hr
u can check all condition

Is this solution Helpfull? Yes (2) | No (1)  

Mahesh  (11 years ago)

There is a small proof that can be helpful for this particular question.

The ratio of times after meeting will be the square of the reciprocal of the ratio of the speeds
So, Aishwarya's time/Abhishek's time = (speed of abhishek)^2/ (speed of aishwarya) ^ 2

The other proof that will help is the time for which they travelled before meeting will be square root of the product of two times

So, from the first one ratio of their speed is 1.5
From the second one, they travelled for 3 hours before meeting

In three, hours with 1.5 times speed abhishek travelled 180 km more.
As the ratio of the distances is also 1.5(based on the speeds), their distances are 540 and 360
As they together covered the total distance , the total distance is 900

Answer is 900

Is this solution Helpfull? Yes (2) | No (1)  

mansi  (11 years ago)

there is one more option 900.....

Is this solution Helpfull? Yes (1) | No   

animesh jian  (11 years ago)

answer is 900.after solve this eq 5x^2-1440x-129600=0 we get x=360 and -72 so the right ans is 900

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

Aditya   (11 years ago)

Answer is 900 or 468?

Is this solution Helpfull? Yes (1) | No   

harsh  (10 years ago)

correct answer:900 km

Is this solution Helpfull? Yes (1) | No   

Digesh Singh Bisht  (2 years ago)

There is a method to find speed ratio by Given time= S1/S2=(T2/T1)Square Root
S1=Speed of Abhishek , T1= Time of Abhishek
S2= Speed of Aishwarya , T2= Time of Aishwarya

Speed Ratio=(4.5/2)^2=3:2

Let the total Distance therefore is X,
3X/5-2X/5=180
X=900 Ans

Is this solution Helpfull? Yes (1) | No   

ROHIT KUMAR  (11 years ago)

ANS-540
--avshek-=(x+180)km---->

Is this solution Helpfull? Yes | No (1)  

Shaibal Dutta  (11 years ago)

as harshvardhan's procss if we put 360 in d eqn we can gt d ansr nd d middl term fctr would be x^2-360x+72x-25920=0 nd atlst d ansr is is 360

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vertika srivastav  (11 years ago)

ans is i think 360

Is this solution Helpfull? Yes | No (7)  

Simran  (10 years ago)

Total travel time=2+4.5-0.5=6 hrs
Distance covered by abhishek is 180km in 2 hrs so his speed becomes 90kmph
therefore distance b/w bang. and kysore will be = 90kmph * 6hr = 540Km.

Is this solution Helpfull? Yes | No (4)  

T.VIGNESWARA REDDY  (10 years ago)

how ever speed of both are not equal but they take same time when first meet so we equal first (x+180/a)=(x/i) after we know time so 2=x/a and 4.5=(x+180)/i after solving we get x=360 so total distance is 2x=180=900 and speed of a is 180 and speed of i is 120 check all conditions with these values it satisfies

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swapnil suman  (9 years ago)

k.Arun gandu jab nehi ata tho solution mat da
m.c

Is this solution Helpfull? Yes | No (1)  

Adil khan  (7 years ago)

guys dont be confuse 900 will be right if u wannb be sure
find speed it will 180kmph and 120kmph
u can put the value nd this will satisfy the condition.
360+360+180=900

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Hassan  (7 years ago)

Time Ratio=(2/4.5)^1/2=2:3
Speed Ratio=3:2
Let X is the total Distance therefore,
3X/5-2X/5=180
X=900

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