Partnership Practice Questions with Detailed Solutions – Level 3

Partnership Level 3 Practice Quiz: Hard Profit-Sharing Problems

Partnership Level 3 is a set of hard arithmetic problems on dividing profit when capital changes during the year, partners join or leave late, or a working partner draws a salary or commission. Aptitude360 gives a worked solution for every question, so you can check each step. Whether you prepare in Chandigarh or anywhere else in India, it builds the multi-step reasoning tougher partnership problems need.

Topics covered in this Partnership Level 3 set

• Capital added or withdrawn partway through the year
• Partners who join late or leave early, and working out when a partner joined
• Working partners who receive a monthly salary, a fixed annual salary or a commission before profit is shared
• Interest on capital paid to each partner before the remaining profit is split
• Finding an unknown capital or time period from a given profit share
• Capitals given as fractions or through linked ratios, and multi-year ventures with staggered entry

Key partnership formulas and rules to remember

• Profit ratio: \( P_{1}:P_{2}=C_{1}T_{1}:C_{2}T_{2} \)
• Changing capital: \( C_{1}t_{1}+C_{2}t_{2} \)
• Share of partner i: \( S_{i}=\dfrac{C_{i}T_{i}}{\sum C_{j}T_{j}}\times P \)
• Capitals from profits and times: \( C_{1}:C_{2}=\dfrac{P_{1}}{T_{1}}:\dfrac{P_{2}}{T_{2}} \)
• Commission of r% on profit after commission: \( \dfrac{r}{100+r}\times P \)

Revision tips for hard partnership problems

• Break each partner's investment into separate periods whenever capital changes, then add the products of capital and time.
• Deduct salary, commission and interest on capital first, and share only the balance in the investment ratio.
• Check whether a commission is charged on the total profit or on the profit left after the commission.
• When a joining time is unknown, write that partner's months as a variable and equate the capital-time ratio to the profit ratio.

Who should take this partnership practice set

This set suits quant aspirants who are already comfortable with basic and moderate partnership problems and now want advanced, multi-step practice.