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In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. lf Abhay doubles his speed, then he would take 1 hour less than Sameer. What is Abhay’s speed? (in km/hr)
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer...
Let Abhay's speed be x km/hr.
View all questions of this test
Then, 30 / x - 30 / 2x = 3
⇒ 6x = 30 ⇒ x = 5km/hr.
Most Upvoted Answer
In covering a distance of 30 km, Abhay takes 2 hours more than Sameer...
To solve this problem, let's assume that Sameer's speed is 'x' km/hr and Abhay's speed is 'y' km/hr.
Given that Abhay takes 2 hours more than Sameer to cover a distance of 30 km, we can write the equation:
30/y = 30/x + 2
Simplifying this equation, we get:
30x = 30y + 2y
30x - 30y = 2y
30(x - y) = 2y
Dividing both sides by 2:
15(x - y) = y
15x - 15y = y
15x = 16y
Now, if Abhay doubles his speed, his new speed would be 2y km/hr. And if he doubles his speed, he would take 1 hour less than Sameer to cover the same distance of 30 km. So we can write the equation:
30/(2y) = 30/x - 1
Simplifying this equation, we get:
30x = 60y - 2y
30x - 60y = -2y
30(x - 2y) = -2y
Dividing both sides by -2:
15(2y - x) = y
30y - 15x = y
30y = 16x
Now, we have two equations:
15x = 16y
30y = 16x
We can solve these equations simultaneously to find the values of x and y.
Dividing the second equation by 2:
15y = 8x
Equating the values of 15x from the first equation and 8x from the second equation:
16y = 8x
16y = 15y
y = x
So, Abhay's speed is equal to Sameer's speed.
Since the options given are in km/hr, we can assume any value for x or y. Let's assume y = 5 km/hr.
Therefore, Abhay's speed is 5 km/hr.
Hence, the correct answer is option D) 5.
Given that Abhay takes 2 hours more than Sameer to cover a distance of 30 km, we can write the equation:
30/y = 30/x + 2
Simplifying this equation, we get:
30x = 30y + 2y
30x - 30y = 2y
30(x - y) = 2y
Dividing both sides by 2:
15(x - y) = y
15x - 15y = y
15x = 16y
Now, if Abhay doubles his speed, his new speed would be 2y km/hr. And if he doubles his speed, he would take 1 hour less than Sameer to cover the same distance of 30 km. So we can write the equation:
30/(2y) = 30/x - 1
Simplifying this equation, we get:
30x = 60y - 2y
30x - 60y = -2y
30(x - 2y) = -2y
Dividing both sides by -2:
15(2y - x) = y
30y - 15x = y
30y = 16x
Now, we have two equations:
15x = 16y
30y = 16x
We can solve these equations simultaneously to find the values of x and y.
Dividing the second equation by 2:
15y = 8x
Equating the values of 15x from the first equation and 8x from the second equation:
16y = 8x
16y = 15y
y = x
So, Abhay's speed is equal to Sameer's speed.
Since the options given are in km/hr, we can assume any value for x or y. Let's assume y = 5 km/hr.
Therefore, Abhay's speed is 5 km/hr.
Hence, the correct answer is option D) 5.
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