Two forces equal to P and 2P newton acts one a particle. If the first be doubled and the second be increased by 20 newton, the direction of the resultant is unaltered. Find the value of P.

If the direction of the resultant force does not change, it means the angle between them remain the same.

Assuming the angle was initially 45 degrees, it will remain the same

Tan 45 = 2p/2p = 1

First force is doubled, it becomes = 4p

20N is added to the second force, it becomes = 2p + 20

Tan 45 = 4p/(2p + 20) = 1

4p = 2p + 20

2p = 20

p = 10