Peter and Paul are partners in a trading firm sharing profits and losses in the ratio of 3… — JAMB UTME

Peter and Paul are partners in a trading firm sharing profits and losses in the ratio of $3:2$ . They admit Grace into the partnership, granting her a $\frac{1}{5}$ share of the total profits. What is the new profit-sharing ratio of Peter, Paul, and Grace?

$12 : 8 : 5$ Answer
B
$3 : 2 : 1$
C
$2 : 2 : 1$
D
$9 : 6 : 5$

Answer

The new profit-sharing ratio of Peter, Paul, and Grace is

12 : 8 : 5

When Grace is admitted with a

\frac{1}{5}

share, the total remaining profit available to Peter and Paul is

1 - \frac{1}{5} = \frac{4}{5}

. Peter's new share is

\frac{3}{5} \times \frac{4}{5} = \frac{12}{25}

, Paul's new share is

\frac{2}{5} \times \frac{4}{5} = \frac{8}{25}

, and Grace's share expressed with the same denominator is

\frac{5}{25}

. Combining these gives the new ratio of

12 : 8 : 5

Step-by-Step Solution

Calculate the remaining profit share after admitting Grace

Remaining share =

1 - \frac{1}{5} = \frac{4}{5}

Grace is given a

\frac{1}{5}

share of the total firm's profit.

Calculate Peter's new share of profit

Peter's share =

\frac{3}{5} \times \frac{4}{5} = \frac{12}{25}

Peter retains his relative proportion of

\frac{3}{5}

out of the remaining

\frac{4}{5}

share.

Calculate Paul's new share of profit

Paul's share =

\frac{2}{5} \times \frac{4}{5} = \frac{8}{25}

Paul retains his relative proportion of

\frac{2}{5}

out of the remaining

\frac{4}{5}

share.

Express Grace's share with a common denominator of 25

Grace's share =

\frac{1}{5} = \frac{5}{25}

A common denominator is required to establish the ratio.

Write the new profit-sharing ratio

Peter : Paul : Grace =

12 : 8 : 5

Comparing the numerators

\frac{12}{25} : \frac{8}{25} : \frac{5}{25}

gives

12 : 8 : 5

Key Concept

Calculation of New Profit Sharing Ratio on Admission of a New Partner

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