Form two places, 60 km apart, A and B start towards each other and meet after 6 hours. Had A travelled with 2/3 of his speed and B travelled with double of his speed, they would have met after 5 hours. The speed of A is:a)4 km/hrb)6 kmphc)10 kmphd)12 kmphCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Let speed of A be a kmph and speed of B be b kmph
Then we have
⇒ a + b = 60/6
⇒ a + b = 10
or 2a + 2b = 20------[1]
also,
⇒ 2/3a + 2b = 60/5 = 12--------------[2]
[1] – [2] leads to
⇒ (4/3)a = 8
a = 6 kmph

Answer

Given information:
- Distance between places A and B = 60 km
- A and B start towards each other and meet after 6 hours
- If A had traveled with 2/3 of his speed and B had traveled with double his speed, they would have met after 5 hours

Let's assume the speed of A as 'x' km/h and the speed of B as 'y' km/h.

Traveling towards each other:
- The relative speed of A and B = x + y
- Time taken to meet = 6 hours

Traveling with adjusted speeds:
- A's adjusted speed = (2/3)x
- B's adjusted speed = 2y
- The relative speed of A and B = (2/3)x + 2y
- Time taken to meet = 5 hours

To find the speed of A, we need to solve these equations.

Solving the equations:
1) Distance = Speed * Time

For the first scenario:
- Distance traveled by A = x * 6
- Distance traveled by B = y * 6

For the second scenario:
- Distance traveled by A = (2/3)x * 5
- Distance traveled by B = 2y * 5

2) Distance traveled by A + Distance traveled by B = Total distance between A and B

For the first scenario:
- x * 6 + y * 6 = 60 (since the total distance between A and B is 60 km)

For the second scenario:
- (2/3)x * 5 + 2y * 5 = 60

Calculating the values:
1) x * 6 + y * 6 = 60
2) (2/3)x * 5 + 2y * 5 = 60

Simplifying equation 2:
- (10/3)x + 10y = 60
- (10/3)x = 60 - 10y
- x = (3/10)(60 - 10y)
- x = 18 - (3/10)y

Substituting the value of x in equation 1:
- 6(18 - (3/10)y) + 6y = 60
- 108 - (9/5)y + 6y = 60
- (9/5)y - 6y = 60 - 108
- (9/5 - 30/5)y = -48/5
- (-21/5)y = -48/5
- y = (-48/5) * (-5/21)
- y = 48/21
- y = 8/3

Substituting the value of y in the equation for x:
- x = 18 - (3/10)(8/3)
- x = 18 - 8/10
- x = 18 - 4/5
- x = (90 - 4)/5
- x = 86/5
- x = 17.2

Therefore, the speed of A is approximately 17.2 km/h. None of the given options match this value, so there may be an error in the given options or the calculations.

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