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And Q are two points, 10 km apart. Anand started from P towards Q and at the same time, Ashok started from Q towards P. They crossed each other after 1 hour. After that, Anand reduced his speed by 2 kmph and Ashok increased his speed by 2 kmph. They reached their destinations simultaneously. Find Anand's initial speed (in kmph).?
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And Q are two points, 10 km apart. Anand started from P towards Q and ...
Problem: Anand and Ashok start from points P and Q respectively, 10 km apart. They move towards each other and cross each other in 1 hour. After that, Anand reduces his speed by 2 kmph and Ashok increases his speed by 2 kmph. They reach their destinations simultaneously. Find Anand's initial speed (in kmph).

Solution:
Let the initial speed of Anand be x kmph.
Let the time taken by Anand to reach the destination be t1 hours.
Let the time taken by Ashok to reach the destination be t2 hours.
Let the speed of Ashok be y kmph.

Step 1: Finding the distance traveled by Anand and Ashok in the first hour.
In the first hour, Anand and Ashok together cover a distance of 10 km (since they cross each other). Let us assume that Anand covers a distance of d km in the first hour, then Ashok covers (10 - d) km in the first hour.

Step 2: Finding the distance traveled by Anand and Ashok in the remaining time.
After the first hour, Anand and Ashok continue to move towards their destinations. Anand reduces his speed by 2 kmph, so his speed becomes (x - 2) kmph. Ashok increases his speed by 2 kmph, so his speed becomes (y + 2) kmph. Since they reach their destinations at the same time, the distance traveled by Anand and Ashok in the remaining time should be the same. Let this distance be D km.

Anand's speed = (x - 2) kmph
Time taken by Anand to travel D km = t1 - 1 hours
Distance traveled by Anand = (x - 2) * (t1 - 1) km

Ashok's speed = (y + 2) kmph
Time taken by Ashok to travel D km = t2 - 1 hours
Distance traveled by Ashok = (y + 2) * (t2 - 1) km

Since the distances traveled by Anand and Ashok are the same, we can equate them:
(x - 2) * (t1 - 1) = (y + 2) * (t2 - 1) ------- (1)

Step 3: Finding the distance traveled by Anand and Ashok in the entire journey.
The total distance traveled by Anand and Ashok in the entire journey is 10 km. Using the values of d and D obtained in steps 1 and 2, we can write:
Distance traveled by Anand = d + (x - 2) * (t1 - 1)
Distance traveled by Ashok = (10 - d) + (y + 2) * (t2 - 1)

Since they reach their destinations simultaneously, the distances traveled by Anand and Ashok should be the same:
d + (x - 2) * (t1 - 1) = (10 - d) + (y + 2) * (t2 - 1)

Simplifying this equation, we get:
d + (x - 2) * (t1 - 1) = 10 - d
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And Q are two points, 10 km apart. Anand started from P towards Q and at the same time, Ashok started from Q towards P. They crossed each other after 1 hour. After that, Anand reduced his speed by 2 kmph and Ashok increased his speed by 2 kmph. They reached their destinations simultaneously. Find Anand's initial speed (in kmph).?
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