AFCAT Numerical Ability · Profit and Loss

Sharing Profit in a Partnership

Partners share profit in the ratio of capital multiplied by time; when everyone invests for the same time, in the ratio of capitals alone.

All Profit and Loss notes

Why this matters

A small page with no AFCAT past-year question, and each row is the dividing skill of Ratio and Proportion applied to money. The marks go on leaving out the time when partners stay for different months, or when one of them takes out part of his capital midway.

Concept 1 of 2: Same period: share by capital

If every partner's money is in the business for the same time, each rupee earns the same share, so the profit splits in the ratio of the capitals.

Definition

Capitals $a : b : c$ and profit $P$ : A's share is $\dfrac{a}{a + b + c} \times P$ , and so on.
Given one partner's share, the total is that share $\times$ (sum of the parts) $\div$ (that partner's parts).
'A's capital is twice B's and three times C's': A = 2B = 3C, so take A as 6, B as 3 and C as 2.
Money taken off the top (to charity, or a manager's salary) comes out before the split.

Share of profit

\text{share of A} = \dfrac{a}{a + b + c} \times P

Worked example

A, B and C invest ₹24,000, ₹36,000 and ₹60,000 for a year. The profit is ₹14,000. Find each share.

Practice this conceptself-check · 3 quick reps

The same idea in a practice question:

Practice questionEasy

Example 1 · Profit and Loss · Partnership and Profit Sharing

Three partners A, B and C invest Rs.

20000

, Rs.

25000

and Rs.

35000

respectively. If the profit at the end of the year is Rs.

9600

, find the difference between the highest and lowest share.

Take out the deduction first

If a share of the profit goes to charity, split only what is left. Applying the partners' ratio to the whole profit overstates every share.

Chained equalities need the LCM

A = 2B = 3C gives

6 : 3 : 2

, not

1 : 2 : 3

. Give A the LCM of 2 and 3 and divide down.

Drill 9 more on same period: share by capital

Concept 2 of 2: Different periods: capital times time

₹1,000 for 6 months earns the same as ₹500 for 12 months. What earns profit is capital multiplied by the months it stays in.

Definition

Shares are in the ratio $a\,t_a : b\,t_b$ .
Capital that changes midway: add the pieces, capital $\times$ months for each stretch.
Working back: the ratio of times is the profit ratio divided by the capital ratio, term by term.
Equal profits mean equal products: $a\,t_a = b\,t_b$ .

Capital times time

\text{A} : \text{B} = a\,t_a : b\,t_b

Worked example

A invests ₹30,000 for 10 months and B invests ₹40,000 for 6 months. Their profit is ₹9,000. Find B's share.

Practice this conceptself-check · 3 quick reps

The same idea in a practice question:

Practice questionEasy

Example 2 · Profit and Loss · Partnership and Profit Sharing

A and B start a business. A invests Rs.

36000

for

12

months and B invests Rs.

48000

for

9

months. If the profit is Rs.

1080

, what is A's share?

Time counts

Equal capitals in for 12 and 8 months share the profit

3 : 2

, not equally.

A withdrawal splits the period

A partner who takes out money midway has two products, one before and one after. Using the starting capital for the whole year overstates his share.

Drill 7 more on different periods: capital times time

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Same period: share by capital
Share of profit
$\text{share of A} = \dfrac{a}{a + b + c} \times P$
Different periods: capital times time
Capital times time
$\text{A} : \text{B} = a\,t_a : b\,t_b$

Drill the questions on this topic