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Two cities A and B are at a distance of 120 km from each other. Two persons P and Q start from First city at a speed of 20km/hr and 10km/hr respectively. P reached the second city B and returns back and meets Q at Y. Find the distance between A and Y.
- a)50 km
- b)66 km
- c)55 km
- d)80 km
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two cities A and B are at a distance of 120 km from each other. Two pe...
P = 120/20 = 6hrs
In 6hrs Q travels 60km
120-60 = 60km
60/(20+10) = 2hrs
Point Y → 60 + 10*2hrs = 80
In 6hrs Q travels 60km
120-60 = 60km
60/(20+10) = 2hrs
Point Y → 60 + 10*2hrs = 80
Most Upvoted Answer
Two cities A and B are at a distance of 120 km from each other. Two pe...
Given:
Distance between city A and B = 120 km
Speed of person P = 20 km/hr
Speed of person Q = 10 km/hr
To find:
Distance between city A and Y
Explanation:
Let's assume that person P takes 't' hours to reach city B and return to city A.
Distance covered by person P in going from A to B = 120 km
Time taken by person P to cover this distance = t/2
∴ Speed of person P = Distance/Time = 120/(t/2) = 240/t
Now, let's assume that person Q takes 't1' hours to reach point Y from city A.
Distance covered by person Q in this time = Speed x Time = 10 x t1
Distance covered by person P in the same time = Speed x Time = 20 x t1
Now, let's assume that person Q takes 't2' hours to reach point Y from city B.
Distance covered by person Q in this time = Speed x Time = 10 x t2
Distance covered by person P in the same time = Speed x Time = 20 x (t - t2)
As both persons meet at point Y, the total distance covered by both persons should be equal.
∴ 10t1 + 10t2 = 20(t - t2)
⇒ 10t1 + 10t2 = 20t - 20t2
⇒ 30t2 = 20t - 10t1
⇒ t2 = (2/3)t - (1/3)t1
Now, the distance between city A and point Y can be calculated as follows:
Distance covered by person Q in going from A to Y = 10t1
Distance covered by person P in going from B to Y = 20(t - t2)
= 20[t - ((2/3)t - (1/3)t1)]
= 20[(1/3)t + (1/3)t1]
Total distance covered = Distance between A and Y
⇒ Distance between A and Y = 10t1 + 20[(1/3)t + (1/3)t1]
= (10/3)t + (10/3)t1
Substituting the value of 't2' in the above equation, we get:
Distance between A and Y = (10/3)t + (10/3)[(2/3)t - (1/3)t1]
= (10/3)t + (20/9)t - (10/9)t1
= (100/27)t - (10/9)t1
To find the value of 't', we can use the fact that person P takes 't' hours to go from A to B and return to A.
Time taken by person P to go from A to B = 120/20 = 6 hours
Time taken by person P to return from B to A = 120/20 = 6 hours
∴ Total time taken by person P = t hours
⇒ t = 6 + 6 = 12 hours
Substituting the value of 't' in the equation for distance, we get:
Distance between A and Y = (100/27) x 12 - (10/9)t
Distance between city A and B = 120 km
Speed of person P = 20 km/hr
Speed of person Q = 10 km/hr
To find:
Distance between city A and Y
Explanation:
Let's assume that person P takes 't' hours to reach city B and return to city A.
Distance covered by person P in going from A to B = 120 km
Time taken by person P to cover this distance = t/2
∴ Speed of person P = Distance/Time = 120/(t/2) = 240/t
Now, let's assume that person Q takes 't1' hours to reach point Y from city A.
Distance covered by person Q in this time = Speed x Time = 10 x t1
Distance covered by person P in the same time = Speed x Time = 20 x t1
Now, let's assume that person Q takes 't2' hours to reach point Y from city B.
Distance covered by person Q in this time = Speed x Time = 10 x t2
Distance covered by person P in the same time = Speed x Time = 20 x (t - t2)
As both persons meet at point Y, the total distance covered by both persons should be equal.
∴ 10t1 + 10t2 = 20(t - t2)
⇒ 10t1 + 10t2 = 20t - 20t2
⇒ 30t2 = 20t - 10t1
⇒ t2 = (2/3)t - (1/3)t1
Now, the distance between city A and point Y can be calculated as follows:
Distance covered by person Q in going from A to Y = 10t1
Distance covered by person P in going from B to Y = 20(t - t2)
= 20[t - ((2/3)t - (1/3)t1)]
= 20[(1/3)t + (1/3)t1]
Total distance covered = Distance between A and Y
⇒ Distance between A and Y = 10t1 + 20[(1/3)t + (1/3)t1]
= (10/3)t + (10/3)t1
Substituting the value of 't2' in the above equation, we get:
Distance between A and Y = (10/3)t + (10/3)[(2/3)t - (1/3)t1]
= (10/3)t + (20/9)t - (10/9)t1
= (100/27)t - (10/9)t1
To find the value of 't', we can use the fact that person P takes 't' hours to go from A to B and return to A.
Time taken by person P to go from A to B = 120/20 = 6 hours
Time taken by person P to return from B to A = 120/20 = 6 hours
∴ Total time taken by person P = t hours
⇒ t = 6 + 6 = 12 hours
Substituting the value of 't' in the equation for distance, we get:
Distance between A and Y = (100/27) x 12 - (10/9)t
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Two cities A and B are at a distance of 120 km from each other. Two persons P and Q start from First city at a speed of 20km/hr and 10km/hr respectively. P reached the second city B and returns back and meets Q at Y. Find the distance between A and Y.a)50 kmb)66 kmc)55 kmd)80 kme)None of theseCorrect answer is option 'D'. Can you explain this answer?
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