Aptitude - Time and Distance - Discussion
Discussion Forum : Time and Distance - General Questions (Q.No. 11)
11.
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Answer: Option
Explanation:
Let Abhay's speed be x km/hr.
Then, | 30 | - | 30 | = 3 |
x | 2x |
6x = 30
x = 5 km/hr.
Discussion:
203 comments Page 1 of 21.
Yamuna said:
4 weeks ago
ta = x+2
ts = x
d = 30 km
Sa = 2Sa , ta = x-1.
Sa = 30/(x+2) --> xSa + 2Sa = 30.
2Sa = 30/(x-1) --> 2xSa - 2Sa = 30.
Since the distance is the same
xSa + 2Sa = 2xSa - 2Sa,
xSa = 4Sa.
x = 4,
ta = x+2,
ta = 6.
s = d/t = 30/6 = 5.
ts = x
d = 30 km
Sa = 2Sa , ta = x-1.
Sa = 30/(x+2) --> xSa + 2Sa = 30.
2Sa = 30/(x-1) --> 2xSa - 2Sa = 30.
Since the distance is the same
xSa + 2Sa = 2xSa - 2Sa,
xSa = 4Sa.
x = 4,
ta = x+2,
ta = 6.
s = d/t = 30/6 = 5.
(3)
Mariyada Ramesh said:
4 months ago
Let Abhay's speed=x, Sameer's time=y
Case 1: 30/x = 2+y.
Case 2: 30/2x = y-1.
30/x-30/2x = (2+y)-(y-1),
= 2+y-y+1,
= 3.
We get the equation:
30/x-30/2x = 3.
By solving we will get the answer.
Case 1: 30/x = 2+y.
Case 2: 30/2x = y-1.
30/x-30/2x = (2+y)-(y-1),
= 2+y-y+1,
= 3.
We get the equation:
30/x-30/2x = 3.
By solving we will get the answer.
(18)
Ayush Kumar Yadav said:
7 months ago
@All.
Here is the explanation:
Let speed of Abhay = t1.
and speed of Sameer = t2.
t1 = t +2 (t is actual Speed).
t2 = t -1 (t is actual speed).
t1 - t2 = t+2 - (t - 1) = 3.
30/x - 30/2x = 3.
30 - 15 = 3x.
15 = 3x.
x = 5 kmh^-1.
Here is the explanation:
Let speed of Abhay = t1.
and speed of Sameer = t2.
t1 = t +2 (t is actual Speed).
t2 = t -1 (t is actual speed).
t1 - t2 = t+2 - (t - 1) = 3.
30/x - 30/2x = 3.
30 - 15 = 3x.
15 = 3x.
x = 5 kmh^-1.
(13)
JaSHaN SaGaR said:
2 years ago
Take the ratio of the speed of Abhay:
1:2
Then the inverse time we get Time ratio,
So:
2:1.
The Gap is 1 unit and this one is given as the sum of hours which is 3 hours.
So 2=6 hours and 1= 3 hours.
So we get the ans by applying a formula that is S= D/T
S= 30/6, which is equal to 5.
1:2
Then the inverse time we get Time ratio,
So:
2:1.
The Gap is 1 unit and this one is given as the sum of hours which is 3 hours.
So 2=6 hours and 1= 3 hours.
So we get the ans by applying a formula that is S= D/T
S= 30/6, which is equal to 5.
(57)
Urvesh Radadiya said:
2 years ago
@All.
My explanation is very simple;
T = D/S.
Suppose the speed of Abhay is x.
First case:
It takes 2 hours more than Samir.
T + 2 = 30/x ---> (1)
Second case:
when speed is double then 2x
it takes 1 hour less so
T-1=30/2x ----> (2)
Compare eq 1 &2;
30/x-2=T.
30/2x+1=T.
30/x-30/2x = 3.
Solving the above eq we get x=5km/h=> Abhay's speed.
My explanation is very simple;
T = D/S.
Suppose the speed of Abhay is x.
First case:
It takes 2 hours more than Samir.
T + 2 = 30/x ---> (1)
Second case:
when speed is double then 2x
it takes 1 hour less so
T-1=30/2x ----> (2)
Compare eq 1 &2;
30/x-2=T.
30/2x+1=T.
30/x-30/2x = 3.
Solving the above eq we get x=5km/h=> Abhay's speed.
(232)
Akshay said:
2 years ago
We know that,
1st case ---> (1)
If Sameer takes 2 hours,
Then, Abhay takes 4 hours.
So,
Sameer takes 2 * 60 = 120 seconds.
&Abhay takes 4 * 60 = 240 seconds.
2nd case ----> (2)
Abhay takes 1hour less than Sameer,
So,
2-1 = 1 * 60 = 60seconds
So,
Abhay's speed is
Case(1)&(2)
240 + 60 = 300Seconds;
Then 300/ 60 = 5.
1st case ---> (1)
If Sameer takes 2 hours,
Then, Abhay takes 4 hours.
So,
Sameer takes 2 * 60 = 120 seconds.
&Abhay takes 4 * 60 = 240 seconds.
2nd case ----> (2)
Abhay takes 1hour less than Sameer,
So,
2-1 = 1 * 60 = 60seconds
So,
Abhay's speed is
Case(1)&(2)
240 + 60 = 300Seconds;
Then 300/ 60 = 5.
(19)
Abhay the guy walking said:
2 years ago
Let's assume that Sameer's speed is S km/h and Abhay's speed is A km/h.
We know that Sameer takes time T to cover 30 km, so:
T = 30/S
We also know that Abhay takes 2 hours longer than Sameer, so:
T + 2 = 30/A
If Abhay doubles his speed, he will cover 30 km in half the time, which is:
T/2
We also know that this time is 1 hour less than Sameer's time, so:
T/2 = T - 1
Solving for T in terms of S:
30/S/2 = 30/S - 1
15/S = 30/S - 1
Multiplying both sides by S(S-15):
15(S-15) = 30(S-15) - S(S-15)
15S - 225 = 30S - 450 - S^2 + 15S
S^2 - 60S + 225 = 0
(S-15)^2 = 0
S = 15 km/h
Now we can use the equation T + 2 = 30/A to solve for Abhay's speed:
T + 2 = 30/A
30/15 + 2 = 30/A
4 = 30/A
A = 7.5 km/h
Therefore, Abhay's speed is 7.5 km/h.
We know that Sameer takes time T to cover 30 km, so:
T = 30/S
We also know that Abhay takes 2 hours longer than Sameer, so:
T + 2 = 30/A
If Abhay doubles his speed, he will cover 30 km in half the time, which is:
T/2
We also know that this time is 1 hour less than Sameer's time, so:
T/2 = T - 1
Solving for T in terms of S:
30/S/2 = 30/S - 1
15/S = 30/S - 1
Multiplying both sides by S(S-15):
15(S-15) = 30(S-15) - S(S-15)
15S - 225 = 30S - 450 - S^2 + 15S
S^2 - 60S + 225 = 0
(S-15)^2 = 0
S = 15 km/h
Now we can use the equation T + 2 = 30/A to solve for Abhay's speed:
T + 2 = 30/A
30/15 + 2 = 30/A
4 = 30/A
A = 7.5 km/h
Therefore, Abhay's speed is 7.5 km/h.
(3)
Krishnan said:
2 years ago
Here's a ChatGpt answer method to solve the problem:
Let's denote Abhay's speed as "a" and Sameer's speed as "s".
We know that distance = speed × time.
According to the problem, Abhay takes 2 hours more than Sameer to cover 30 km. So, we can write:
30 = s × (t + 2) (Equation 1)
where t is Sameer's time taken to cover the distance.
If Abhay doubles his speed, he would take 1 hour less than Sameer to cover 30 km. So, we can write:
30 = 2a × (t - 1) (Equation 2)
where t - 1 is Abhay's time taken to cover the distance at double the speed.
Now, we can solve these two equations for a and s:
From Equation 1, we get:
t = (30/s) - 2
Substituting this value of t in Equation 2, we get:
30 = 2a × ((30/s) - 3).
Simplifying this equation, we get:
a = (45s)/(4s - 60).
Now, substituting this value of a in Equation 1, we get:
30 = s × ((30/s) + 2).
Simplifying this equation, we get:
s^2 = 450.
Therefore, s = 15 km/h.
Substituting this value of s in the expression for a, we get:
a = (45 × 15)/(4 × 15 - 60) = 45 km/h
Therefore, Abhay's speed is 45 km/h.
Let's denote Abhay's speed as "a" and Sameer's speed as "s".
We know that distance = speed × time.
According to the problem, Abhay takes 2 hours more than Sameer to cover 30 km. So, we can write:
30 = s × (t + 2) (Equation 1)
where t is Sameer's time taken to cover the distance.
If Abhay doubles his speed, he would take 1 hour less than Sameer to cover 30 km. So, we can write:
30 = 2a × (t - 1) (Equation 2)
where t - 1 is Abhay's time taken to cover the distance at double the speed.
Now, we can solve these two equations for a and s:
From Equation 1, we get:
t = (30/s) - 2
Substituting this value of t in Equation 2, we get:
30 = 2a × ((30/s) - 3).
Simplifying this equation, we get:
a = (45s)/(4s - 60).
Now, substituting this value of a in Equation 1, we get:
30 = s × ((30/s) + 2).
Simplifying this equation, we get:
s^2 = 450.
Therefore, s = 15 km/h.
Substituting this value of s in the expression for a, we get:
a = (45 × 15)/(4 × 15 - 60) = 45 km/h
Therefore, Abhay's speed is 45 km/h.
(2)
Niraj katwal said:
2 years ago
Let the speed of Sameer be x.
Then, Ajay's speed = x+2.
When Ajay doubles his speed,
2(x+2) = x -1
or,2x+4 = x-1
Since speed can never be negative.
x=5.
Then, Ajay's speed = x+2.
When Ajay doubles his speed,
2(x+2) = x -1
or,2x+4 = x-1
Since speed can never be negative.
x=5.
(97)
Gramophone said:
2 years ago
t+2 = 30/s ----> 1
t-1 = 30/2s ---- > 2
Solving this equation, we get;
s = 5.
t-1 = 30/2s ---- > 2
Solving this equation, we get;
s = 5.
(29)
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