Jennifer has $400 more than Brian has. If she were to give Brian 20%

There are 2 ways of going about. First is the method of equations and the second is by using the options.


Let the amount of money with Brian = x

Therefore the amount with Jennifer = x + 400

If Jennifer gives 20% away, then amount given to Brian = 0.2 * (x + 400) = 0.2x + 80

Amount with Brian now = x + 0.2x + 80 = 1.2x + 80

The remaining amount with Jennifer = 80% of (x + 400) = 0.8x + 320


Given that Brian has 2/3 rd of what Jennifer has, i.e 1.2x + 80 = \(\frac{2}{3}\) * (0.8x + 320)

Solving for x, we get 3(1.2x + 80) = 2(0.8x + 320)

3.6x + 240 = 1.6x + 640

2x = 400

x = 200


The second method is using the options. Since the options give us the amount Brian has initially, we can calculate and see which option matches the requirements.
We need to calculate Jennifer's final amount and see if it is divisible by 3, as Brian will have 2/3rd of that amount


Option A: B = 100, J = 100 + 400 = 500

Brians final amount = 100 + 20% of 500 = 200

Jennifers final amount = 80% of 500 = 400. Now this is not divisible by 3, so this option gets eliminated.



Option B: B = 120, J = 120 + 400 = 520

Brians final amount = 100 + 20% of 520 = 204

Jennifers final amount = 80% of 520 = 416. This is not divisible by 3, so this option gets eliminated.


Option C: B = 160, J = 160 + 400 = 560

Brians final amount = 100 + 20% of 560 = 212

Jennifers final amount = 80% of 560 = 448. This is not divisible by 3, so this option gets eliminated.



Option D: B = 180, J = 180 + 400 = 580

Brians final amount = 100 + 20% of 580 = 216

Jennifers final amount = 80% of 580 = 464. This is not divisible by 3, so this option gets eliminated.




Option E

Arun Kumar