Aptitude - Problems on Trains - Discussion
Discussion Forum : Problems on Trains - General Questions (Q.No. 31)
31.
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Answer: Option
Explanation:
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3.
Discussion:
109 comments Page 5 of 11.
Arshad Ansari said:
8 years ago
Let the train meet after time t at point O and train from Howrah to Patna travels X1 distance with speed v1 and train from Patna travels X2 distance with speed v2 to reach O.
X2=9 *v1 ; X1= 16*v2
and X1 = t*v1 ; X2= t*v2.
From above equations
16* V2^2=9*V1^2,
V1/V2=4/3.
X2=9 *v1 ; X1= 16*v2
and X1 = t*v1 ; X2= t*v2.
From above equations
16* V2^2=9*V1^2,
V1/V2=4/3.
Ishu shrivastava said:
6 years ago
Solving the eqns..
D=(v1+v2)t ---------> 1
D=(t+9)v1---------> 2
D=(t+16)v2---------> 3.
Putting the value of t from eq 1 in eq 2 & 3 then taking all the term having D on one side and then taking ratio of eq.2 & 3.
And we will get v1/v2=√16/√9= 4/3.
D=(v1+v2)t ---------> 1
D=(t+9)v1---------> 2
D=(t+16)v2---------> 3.
Putting the value of t from eq 1 in eq 2 & 3 then taking all the term having D on one side and then taking ratio of eq.2 & 3.
And we will get v1/v2=√16/√9= 4/3.
(1)
Pratham said:
1 decade ago
Hey guys sorry to interrupt.
Even I didn't understood why we used square root, its formula I can understand.
Its clear that S1=>9, S2=>16.
Then how could S1/S2=>3/9.
Its not possible 9/16 = 3/4.
Can any 1 explain it better? Really confused.
Even I didn't understood why we used square root, its formula I can understand.
Its clear that S1=>9, S2=>16.
Then how could S1/S2=>3/9.
Its not possible 9/16 = 3/4.
Can any 1 explain it better? Really confused.
Chara said:
1 decade ago
Two things strikes out here:
1. Just memorize the formula and save your time.
2. By logic, the answer has to be 4:3 coz this is the only option with speed of train A more than the train B, and from the question, we know train A is faster than train B.
1. Just memorize the formula and save your time.
2. By logic, the answer has to be 4:3 coz this is the only option with speed of train A more than the train B, and from the question, we know train A is faster than train B.
Praful lahoti said:
8 years ago
Ratio of time of A and B =9:16.
Then the ratio of distance is the reverse of the ratio of time because when the time of A is less than B to cover a distance than the speed of A is greater than B so the ratio of the speed of A:B=16:9.
Simply A:B=4:3.
Then the ratio of distance is the reverse of the ratio of time because when the time of A is less than B to cover a distance than the speed of A is greater than B so the ratio of the speed of A:B=16:9.
Simply A:B=4:3.
Yashwant Singh said:
3 years ago
Let v be the speed of train 1 (H to P) and u be the speed of train 2(P to H).
Time taken by both trains to meet is equal; so,
x/v = y/u.
Also,
9 = y/v and 16 = x/u.
=> y=9v and x=16u.
put in first eqn;
16u/v=9v/u.
(v/u)^2 = 16/9.
v/u = 4/3.
Time taken by both trains to meet is equal; so,
x/v = y/u.
Also,
9 = y/v and 16 = x/u.
=> y=9v and x=16u.
put in first eqn;
16u/v=9v/u.
(v/u)^2 = 16/9.
v/u = 4/3.
(27)
C ASIF ALI said:
7 years ago
@All.
LOGICAL WAY:
if train1 reaches in 9hrs and train 2 reaches in 16hrs.
That means the speed of train 1 > speed of train 2.
Now cross check the answers. Only option B has a train1 speed greater than train2. i.e 4:3.
LOGICAL WAY:
if train1 reaches in 9hrs and train 2 reaches in 16hrs.
That means the speed of train 1 > speed of train 2.
Now cross check the answers. Only option B has a train1 speed greater than train2. i.e 4:3.
(3)
Gopinadh said:
4 years ago
@All.
We know that speed =distance/time.
If the ratio of the speeds of A and B is a : b, then the ratio of
The times taken by them to cover the same distance is 1/a : 1/b or b: a. Because the distance travelled is the same.
We know that speed =distance/time.
If the ratio of the speeds of A and B is a : b, then the ratio of
The times taken by them to cover the same distance is 1/a : 1/b or b: a. Because the distance travelled is the same.
(6)
Shubham Rishishwar said:
1 decade ago
Howrah A--> B<--Patna
|--Va*t----->|<---Vb*t--|
|<--Tb = 16hr--|--Ta=9hr->|
Va = (Vb*t)/9 --- Eq1
Vb = (Va*t)/16 --- Eq2
Eq1/Eq2
(Va/vb) = (Vb/Va)*(16/9)
(Va:Vb) = sqrt(16/9) = 4:3.
|--Va*t----->|<---Vb*t--|
|<--Tb = 16hr--|--Ta=9hr->|
Va = (Vb*t)/9 --- Eq1
Vb = (Va*t)/16 --- Eq2
Eq1/Eq2
(Va/vb) = (Vb/Va)*(16/9)
(Va:Vb) = sqrt(16/9) = 4:3.
Harshit said:
1 decade ago
(x+y)/(s1+s2) = x/s1 = y/s2;
x/s2 = 9;
y/s1 = 16;
Hence s1/s2 = 3/4;
Where <----------x-------->|<--------y------->.
<----------------TOTAL----------------->.
->s1 s2<-.
x/s2 = 9;
y/s1 = 16;
Hence s1/s2 = 3/4;
Where <----------x-------->|<--------y------->.
<----------------TOTAL----------------->.
->s1 s2<-.
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