The partners are liable for income/expenditure/profit/loss as per their percentage holding of the business or their partnership percentage. This is defined by their capital/work/other things contribution in terms of time. The partnership terms can be of many types, in questions you may encounter partners putting monies for different time periods, which can be calculated by multiplying the money with the time in months, the money has been invested for.

### Quicker Method to Solve the Questions

If the period of investment is the same for each partner, then the profit or loss is divided in the ratio of their investments.

If A and B are partners in a business, then

If A, B and C are partners in a business, then

Investment of A : Investment of B : Investment of C

= Profit of A : Profit of B : Profit of C, or

= Loss of A : Loss of B : Loss of C

**Solution:** If total profit is x, then

A’s share

= of the balance

⇒

⇒ 14x + 27x = 369 × 140

⇒

B’s share

= Rs. 405

C’s share

= Rs. 486

If the period of investment is different, then the profit or loss is divided in the ratio of their Monthly Equivalent Investment.

= or

i.e.,

or

**If A, B and C are partners in a business, then:**

Monthly Equivalent Investment of A : Monthly Equivalent Investment of B : Monthly Equivalent Investment of C

= Profit of A : Profit of B : Profit of C.

= Loss of A : Loss of B : Loss of C.

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**Solution:** Monthly equivalent rent of A = 126 × 3 = 378

Monthly equivalent rent of B = 162 × 5 = 810

Monthly equivalent rent of C = 216 × 4 = 864

∴ Rent is to be divided in the ratio 378 : 810 : 864,

ie. 7 : 15 : 16

∴ A would have to pay of the rent

of the rent

= Rs. 105

∴ B would have to pay of the rent

= Rs. 225

and C would have to pay ,

i.e. of the rent

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