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:
5 kmph
6 kmph
6.25 kmph
7.5 kmph
Answer: Option
Explanation:

Let Abhay's speed be x km/hr.

Then, 30 - 30 = 3
x 2x

6x = 30

x = 5 km/hr.

Discussion:
200 comments Page 1 of 20.

JaSHaN SaGaR said:   10 months 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.
(32)

Urvesh Radadiya said:   11 months 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.
(137)

Akshay said:   1 year 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.
(14)

Abhay the guy walking said:   1 year 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.
(2)

Krishnan said:   1 year 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.
(2)

Niraj katwal said:   1 year 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.
(62)

Gramophone said:   1 year ago
t+2 = 30/s ----> 1
t-1 = 30/2s ---- > 2

Solving this equation, we get;
s = 5.
(23)

Jabir said:   2 years ago
@All.


Here, is my explanation;

When Abhay moves at normal speed;

Let the time taken by Sameer, time = X.
Then, Abhay needs 2 more hours time than Sameer. ie...time=X+2.
Consider the speed of Abhay, speed =Y

Now, Abhay moves at double speed, so he reaches 1 hour before Sameer.

So speed becomes speed=2Y and time =X-1

Now you can make the equation for distance
Distance is already given d=30

Case 1 (during the normal speed of Abhay)
Distance =speed*time
ie...30=Y*(X+2)----> equation 1

Similarly,
Case 2(during the double speed of Abhay)
30=2Y*(X-1)--->equation 2

Now solve equations 1 and 2 with your logic;
You, will get the answer 5.
(22)

Sarang said:   2 years ago
d = (s1*s2*time diff)/( s1-s2).
30 = x * 2x * 3/x * 2x.
x = 5.
(7)

Anomie said:   2 years ago
Good explanation. Thanks all.
(4)


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