P and 2P are two forces acting on a particle. When the first force in increased by 20 Kg-wt and the second force is doubled,the direction of resultant force remains uncharged. Find P.

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Solution

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

$tan 45^{0} = \frac{2 P}{2 P} = 1$

Now, first force is double

So, force $= 4 P$

20 N is added to the second force

Then, force $= 2 P + 20$

Now,

$tan 45^{0} = \frac{4 P}{2 P + 20}$

$\frac{4 P}{2 P + 20} = 1$

$2 P = 20$

$P = 10 N$

Hence, this is the required solution

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