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Two places P and Q are 440 km apart. Anuj starts from point P towards Q and Dia starts from point Q towards P and they meet after 8 hours. After meeting, Anuj decreased his speed by 9 km/hr and Dia increased her speed by 9 km/hr, then they reached their respective destination at the same time. What is the initial speed of Dia?

Two places P and Q are 440 km apart. Anuj starts from point P towards Q and Dia starts from point Q towards P and they meet after 8 hours. After meeting, Anuj decreased his speed by 9 km/hr and Dia increased her speed by 9 km/hr, then they reached their respective destination at the same time. What is the initial speed of Dia? Correct Answer 23 km/hr

Since Anuj and Dia are travelling towards each other, the relative speed must be the sum of the speed of Anuj and Dia;

Suppose the speeds of Anuj and Dia are ‘A’ and ‘D’ km/hr respectively;

∴ (A + D) = 440/8

⇒ (A + D) = 55   ---- (1)

After meeting, Anuj decreased his speed by 9 km/hr and Dia increased her speed by 9 km/hr then they reached their respective destination at the same time;

This is possible only if the new speed of Anuj becomes equal to the initial speed of Dia and vice versa.

∴ (A - D) = 9   ---- (2)

Solving both the equations∶

⇒ A = 32 and B = 23

∴ Initial speed of Dia = 23 km/hr

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