Question

A sum of 7700 is to be divided among three brothers zain, zaid and zohaib in such a away that simple interest on each part at 5% per annum after 1, 2 and 3 years, respectively remains equal. The share of zain is more than that of zohaib by:
a) 2800
b) 2500
c) 3000

Answer 1

@KamiBug

Answer 2

This question is more complicated than I thought it would be.

Trying to come up with an equation. How do you think we should start?

Answer 3

As far as i think the equation could be like this one,
Let x,y and z be the amounts the have, so
0.05x=(2).05y=(3)0.05z

Answer 4

I'm think I see what you are doing

A = X e^rt r =0.05 t = 1 Interest = X -A
A = Y e^rt r =0.05 t = 2 Interest = Y -A
A = Z e^rt r =0.05 t = 3 Interest = Z -A

the interest is the same for each brother

Answer 5

Yes but what next??

Answer 6

Maybe setting the first and last equations (we don't care about the middle brother) interest equal to each other and solve for X or Z.

I need to work it out on paper to be sure.

Answer 7

Sorry I am not seeing this solution. I need to walk away and think about it some more, maybe the solution will come to me.

Answer 8

Okay. If you get to the solution do tell me.

Answer 9

You do have to factor in the third brother, in order to get the amount correct.

Answer 10

And how are we gonna do that?

Answer 11

@rebeccaxhawaii

Answer 12

Okay. I used an alternate method to solve the problem, in order to give me some insight to how the equation might work.

I used excel, created the simple interest equations for the three brothers for various values that summed to 7700. And zeroed in the the accrued interests until the differences were less than a penny or so.

It is a not good math, but as an retired engineer, it solves the question.

I will attach a picture of the excel, if you don't want to see the answer. Don't look.

Answer 13

@TrojanPoem

Answer 14

Could not use this method to solve this. But thanks anyways for all the help

Answer 15

@retirEEd hey I tried to PM you but you have everyone blocked. I was wondering if you could help me with my problem

Answer 16

HEY I think I solved the equation! Working on the final answer, now. Want to verify before I post it.

If I'm right, we were very close and I apologize for not seeing it sooner.

Answer 17

The first thought was incorrect, an error in logic

However a revision worked perfectly.... I see you are offline but I will post anyways

(Interest originally incorrect I had X - A, Y - A and Z - A)
A
A = X e^0.05 Interest = A - X so I = X e^0.05 - X I = X (e^0.05 - 1)
A = Y e^0.1 Interest = A - Y so I = Y e^0.1 - Y I = Y (e^0.1 - 1)
A = Z e^0.15 Interest = A - Z so I = Z e^0.15 - Z I = Z (e^0.15 - 1)

ALL of the I s are equal and X + Y + Z = 7700
Solve the first two Is for Y and the first and third I for Z

Y = X (e^0.05 - 1) / (e^0.1 - 1)
Z = X (e^0.05 - 1) / (e^0.15 - 1)

Plug into X + Y + Z = 7700

7700 = X + X (e^0.05 - 1) / (e^0.1 - 1) + X (e^0.05 - 1) / (e^0.15 - 1)

7700 = X [ 1 + (e^0.05 - 1) / (e^0.1 - 1) + (e^0.05 - 1) / (e^0.15 - 1)]

Solve for X = 7700 / [ 1 + (e^0.05 - 1) / (e^0.1 - 1) + (e^0.05 - 1) / (e^0.15 - 1)]

= 7700 / 1.804315007 (the key punching get hairy)

= 4267.547 which is fairly close to my excel answer

Follow a similar process to get Z (the third brother)
obviously the difference is X -Z