Partnership Practice Questions Level 2 on Capital and Time Ratios
This Level 2 partnership set builds the skill of dividing profit in the ratio of capital multiplied by time. It covers partners joining late or leaving early, capital added or withdrawn midway, working partner salaries and finding an unknown investment or period. Aptitude360 includes a worked solution for every question.
Partnership topics in this Level 2 set
- Profit sharing when capitals and periods differ
- Partners who join after some months or leave before the year ends
- Capital added or withdrawn partway through the year
- Working partner paid a monthly salary or a share of profit before division
- Finding an unknown investment from a partner's share
- Finding the joining month or investment period from capital and profit ratios
Key partnership formulas
- Profit ratio: \( P_{1}:P_{2}=C_{1}T_{1}:C_{2}T_{2} \)
- Partner's share: \( \text{Share}=\dfrac{C_{1}T_{1}}{C_{1}T_{1}+C_{2}T_{2}}\times P \)
- Period ratio: \( \dfrac{T_{1}}{T_{2}}=\dfrac{P_{1}}{P_{2}}\times\dfrac{C_{2}}{C_{1}} \)
- Changed capital: \( \text{Total capital-time}=C_{a}t_{a}+C_{b}t_{b} \)
- After salary: \( \text{Divisible profit}=P-\text{Salary} \)
Revision tips for partnership problems
- Convert every investment into capital multiplied by months before forming the ratio
- Split the year into periods whenever capital changes and add the products
- Deduct the working partner's salary or commission first, then divide the rest
- Cancel common factors in capital-time products to keep ratios small
Who should practise this partnership set
It suits arithmetic learners who know the basic profit ratio and are ready for intermediate problems with changing capital and working partners.