Sandro, Tasos, and Ursula invested in a business. Five years

Question

Sandro, Tasos, and Ursula invested in a business. Five years later, they sold the business and divided the proceeds, allocating 1/6 equally among them and the remaining 5/6 in proportion to their initial investments. If, in total, Tasos received 1/4 more than Sandro and Ursula combined, what fraction of the original capital did Tasos contribute?

A) 1/2
B) 3/5
C) 2/3
D) 3/4
E) 5/6

Inspired by Bunuel

A) 1/2
B) 3/5
C) 2/3
D) 3/4
E) 5/6

Inspired by Bunuel

Dereno · Answer

Let the total amount be 54x.

(1/6) of the amount ,denotes the proceeds = (1/6)*54x = 9x.

This amount is divided equally among three persons : Sandro, Tasos and Ursula.

So, that each gets 3x among the three.

Remaining (5/6)* 54x = 45x is distributed among the three based on the proportion to their initial investments.

In total , the amount received by Tacos = 1+ (1/4) ( Sandro + Ursula)

So,  Tacos : ( Sandro + Ursula) = 5 : 4

The total 9 units = 54x. So, 1 unit = 6x.

Therefore , the total amount received by Tacos : ( Sandro+ Ursula) = 30x : 24x

Amount received by Tacos in proportion to their investment = 30x - 3x = 27x

The amount received by (Sandro + Ursula) in proportion to their investment = 45x -27x = 18x

Fraction of original capital Tacos receive = 27x / 45x =  3/5

Option B

Aman2487 · Answer

Can you please elaborate how you took 54x as total amount

Dereno · Answer

The fractions has a denominator value of 6 initially.

In mid of the question, it’s mentioned tacos received 1/4 more than (Sandro and Ursula). 1+(1/4)= (5/4)

So the ratio of Tacos : (Sandro and Ursula) = 5:4

So, we have a total part of 9. Here, we need to have a multiple which is divisible by 9. At the beginning it’s a multiple of 6.

So, took it as 54x for convenience to avoid fractions. Working with fractions is tedious and prone to error at times.

Hope this clarifies ur doubts.

Aman2487 · Answer

Hi but the question asks what fraction of the original capital did Tasos contribute? 
However the solution in the end devides money recived by tacos depending on the proportion to money received in total by all 3 ( in proportion )
 
Question says 
What fraction of the orignal capital won't that mean the amount he contributed to wards his initial investment

Aman2487 · Answer

Hi but the question asks what fraction of the original capital did Tasos contribute? 
However the solution in the end devides money recived by tacos depending on the proportion to money received in total by all 3 ( in proportion )
 
Question says 
What fraction of the orignal capital won't that mean the amount he contributed to wards his initial investment

Dereno · Answer

The extract from question stem :

Five years later,   they sold the business and divided the proceeds  , allocating 1/6 equally among them

and   the remaining   5/6 in proportion to their initial investments.

It’s not the total 54x which is being divided.

The initial investments is proportional to (5/6)*54x = 45x.

The question is worded in a manner to make mistakes.

Sandro, Tasos, and Ursula invested in a business. Five years

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Sandro, Tasos, and Ursula invested in a business. Five years

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