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If two person A and B start at the same time in an opposite direction from two points and after passing each other they complete the journey in a and b hours respectively, then the ratio of A’s and B’s speed will be:
- a)√a : √b
- b)√b: √a
- c)√a + √b: √a - √b
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If two person A and B start at the same time in an opposite direction...
Let total distance be D km and A’s speed be x km/hr, and B’s speed be y km/hr.
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If two person A and B start at the same time in an opposite direction...
Given information:
- Person A and person B start at the same time in opposite directions from two points.
- After passing each other, person A completes the journey in 'a' hours.
- After passing each other, person B completes the journey in 'b' hours.
To find:
The ratio of A's and B's speed.
Explanation:
Let the distance between the two points be 'd'.
Let the speeds of person A and person B be 'vA' and 'vB' respectively.
1. Distance travelled by person A in 'a' hours:
Distance = Speed × Time
Distance travelled by person A = vA × a
2. Distance travelled by person B in 'b' hours:
Distance travelled by person B = vB × b
3. When person A and person B pass each other, the total distance travelled by both will be equal to the total distance between the two points, i.e., d.
So, we have the equation:
vA × a + vB × b = d
4. To find the ratio of A's and B's speeds, we can divide the above equation by vB × a:
(vA × a + vB × b) / (vB × a) = d / (vB × a)
5. Simplifying the equation:
(vA × a) / (vB × a) + (vB × b) / (vB × a) = d / (vB × a)
vA / vB + b / a = d / (vB × a)
6. Since person A and person B start at the same time, the ratio of their times will be equal to the ratio of their speeds:
a / b = vB / vA
7. Substituting the value of a / b in equation 5:
vA / vB + (vB × b) / (vB × a) = d / (vB × a)
vA / vB + 1 = d / (vB × a)
8. Rearranging the equation:
vA / vB = d / (vB × a) - 1
vA / vB = (d - vB × a) / (vB × a)
9. Since person A and person B start at the same time, the distance travelled by person A before meeting person B will be equal to the distance travelled by person B before meeting person A.
Therefore, d - vB × a = vA × a
d = vA × a + vB × a
d = (vA + vB) × a
10. Substituting the value of d in equation 8:
vA / vB = ((vA + vB) × a) / (vB × a) - 1
vA / vB = (vA + vB) / vB - 1
vA / vB = vA / vB + 1 - 1
vA / vB = 1
Conclusion:
The ratio of A's and B's speed is 1, which can be represented as √b : √a.
- Person A and person B start at the same time in opposite directions from two points.
- After passing each other, person A completes the journey in 'a' hours.
- After passing each other, person B completes the journey in 'b' hours.
To find:
The ratio of A's and B's speed.
Explanation:
Let the distance between the two points be 'd'.
Let the speeds of person A and person B be 'vA' and 'vB' respectively.
1. Distance travelled by person A in 'a' hours:
Distance = Speed × Time
Distance travelled by person A = vA × a
2. Distance travelled by person B in 'b' hours:
Distance travelled by person B = vB × b
3. When person A and person B pass each other, the total distance travelled by both will be equal to the total distance between the two points, i.e., d.
So, we have the equation:
vA × a + vB × b = d
4. To find the ratio of A's and B's speeds, we can divide the above equation by vB × a:
(vA × a + vB × b) / (vB × a) = d / (vB × a)
5. Simplifying the equation:
(vA × a) / (vB × a) + (vB × b) / (vB × a) = d / (vB × a)
vA / vB + b / a = d / (vB × a)
6. Since person A and person B start at the same time, the ratio of their times will be equal to the ratio of their speeds:
a / b = vB / vA
7. Substituting the value of a / b in equation 5:
vA / vB + (vB × b) / (vB × a) = d / (vB × a)
vA / vB + 1 = d / (vB × a)
8. Rearranging the equation:
vA / vB = d / (vB × a) - 1
vA / vB = (d - vB × a) / (vB × a)
9. Since person A and person B start at the same time, the distance travelled by person A before meeting person B will be equal to the distance travelled by person B before meeting person A.
Therefore, d - vB × a = vA × a
d = vA × a + vB × a
d = (vA + vB) × a
10. Substituting the value of d in equation 8:
vA / vB = ((vA + vB) × a) / (vB × a) - 1
vA / vB = (vA + vB) / vB - 1
vA / vB = vA / vB + 1 - 1
vA / vB = 1
Conclusion:
The ratio of A's and B's speed is 1, which can be represented as √b : √a.
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If two person A and B start at the same time in an opposite direction from two points and after passing each other they complete the journey in a and b hours respectively, then the ratio of A’s and B’s speed will be:a)√a : √bb)√b: √ac)√a + √b: √a - √bd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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