Question

at the beginning of war, the number of war planes possessed by two powers are in the ratio of 1.6:1,the weaker power having 400. in a general engagement, each power loses the same number of planes but, the ratio is changed to 2:1. how many planes does each lose?​

Answer 1

Answer:

Step-by-step explanation:

Given

Initial ratio of planes possessed by two powers,

Planes owned by strong power:Planes owned by weak power= 1.6:1

Let planes owned by strong power be X

Therefore by given condition

X:400(planes owned by weak)=1.6:1

X/400=1.6/1

X x 1 = 1.6 X 400

X = 640

Therefore initial number of planes owned by strong is 640

It is given that after war they Lose same number of planes and their ratio of planes becomes 2:1.

Let the number of planes lost by both powers be k.

Therefore,

640-k:400-k = 2:1

640-k/400-k=2/1

640-k = 2(400-k)

640-k= 800-2k

-k+2k= 800-640

k=160

Therefore planes lost by both powers is 160

Answer 2

Answer:

x=400

y=160

ratio=2:1

Step-by-step explanation:

Let

First power have planes = 1.6(x)

Second power have planes = x

Then

Ratio will have be 1.6(x): x = 1.6: 1

Now

According to the condition

less power have planes = 400

And

Since 1.6 > 1

So

X = 400

And

Second power have planes = 1.6(400) = 640

Now

According to the second condition

If y numbers planes loss then the new ratio is

2:1

And

So

640 - y: 400- y = 2:1

This simplies that

640 - y = 2(400 - y)

640 - y = 800 - 2y

2y - y = 800 - 640

y = 160

So

160 planes loss by both to get new ratio 2: 1

Checking:

640-160 480

400-160 = 240

And

480: 240 = 480 / 240 = 2/1