Three business partners, X, Y, and Z, invest in a venture. X contributes \frac{1}{3} of th… — JAMB UTME

Three business partners, $X$ , $Y$ , and $Z$ , invest in a venture. $X$ contributes $\frac{1}{3}$ of the total capital for $\frac{1}{4}$ of the total duration of the business. $Y$ contributes $\frac{1}{4}$ of the capital for $\frac{1}{2}$ of the duration, while $Z$ contributes the remaining capital for the entire duration. If the total profit realized from the business is $\mathcal{N}78,000$ , what is $Z$ 's share of the profit?

A
$\mathcal{N}32,500$
B
$\mathcal{N}26,000$
$\mathcal{N}52,000$ Answer
D
$\mathcal{N}60,000$

Answer

\mathcal{N}52,000

Profit distribution in compound partnerships depends on both capital invested and investment time duration.

X

's product is

\frac{1}{12}

Y

's product is

\frac{1}{8}

, and

Z

's product is

\frac{5}{12}

. Scaling these by 24 gives a ratio of

2 : 3 : 10

. With 15 total parts,

Z

receives

\frac{10}{15}

\mathcal{N}78,000

, which equals

\mathcal{N}52,000

Step-by-Step Solution

Determine

Z

's fraction of the total capital

Z

's capital fraction

= 1 - \left(\frac{1}{3} + \frac{1}{4}\right) = 1 - \frac{7}{12} = \frac{5}{12}

The sum of all capital contributions must equal 1.

Calculate the compound product of (Capital Share

\times

Time Duration) for each partner

X = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}

Y = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}

Z = \frac{5}{12} \times 1 = \frac{5}{12}

Profit sharing in compound partnerships is proportional to the product of capital invested and the time period.

Convert the fractions to an equivalent integer ratio

Multiplying

\frac{1}{12} : \frac{1}{8} : \frac{5}{12}

by 24 gives the ratio

2 : 3 : 10

Finding the least common multiple (24) simplifies the fractions into integer ratio parts.

Compute

Z

's profit share from the total profit

Total ratio parts

= 2 + 3 + 10 = 15

Z

's share

= \frac{10}{15} \times \mathcal{N}78,000 = \mathcal{N}52,000

Multiply total profit by

Z

's ratio fraction.

Key Concept

Compound Ratio and Partnership Profit Sharing

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic