Henry Ernest Dudeney/Puzzles and Curious Problems/6 - A New Partner/Solution

by : $6$

 * A New Partner

Solution
Rogers pays $\pounds 500$ to Smugg and $\pounds 2000$ to Williamson.

Proof
The assumption that must be made is that the contribution of Rogers is one third of the total business value before he entered.

Let $T$ pounds be the total investment in the business.

Let $S$ and $W$ pounds be the amounts of capital invested by Smugg and Williamson respectively.

We have:

So Rogers pays $\pounds 500$ to Smugg and $\pounds 2000$ to Williamson.