Partnership Questions and Shortcut Tricks

Partnership Solved Examples - Page 2
Partnership Important Questions - Page 3

When two or more than two persons run a business jointly. They are called partners and the deal is known as partnership. Partnership is of two kinds : (i) Simple and (ii) Compound.

Simple Partnership : If the capitals of the partners are invested for the same period the partnership is called simple.

Rule. When investment of all the partners are for the same time, the profit or loss is divided among them in the ratio of their investments.

Compound Partnership : If the capitals of the partners are invested for different lengths of time, the partnership is called compound.
Rule. When investment are for different times then equivalent capitals are calculated for a unit of time by multiplying the capital with the number of units of time. The profit or loss is now divided in the ratio of these capitals.

Note I. If A and B invested their capitals for different length of time, then Images
Note II. A partner who manages the business is called a working partner and the one who simply invests the money is called a sleeping partner.
Note III. In every examination the questions are generally set on compound partnership. But such questions are first converted into simple partnership and then solved.

 

Partnership Important Examples

Example 1. A and B started a business in partnership with Rs.50,000 and Rs.60,000 respectively. A is also a working partner and gets 10% of the total profit for looking after the business. How much is the share or B less than the share of A in the profit of Rs.55,000 ?

Solution : Ratio of two Capital of A and B
= 50,000 : 60,000
= 5 : 6
\because A gets 10% of the total profit for looking after the business.
\therefore Income received by A for looking after the business.
= 10% Rs.55, 000
= Rs. 5500
Rest of the profit
= 55,000 – 5500
= Rs. 49500

Now, from this amounts of profit A and B will get their shares of profit in the ratio of their invested capitals.
Profit received by
A = 49,500\times \frac{5}{11}
= Rs.22,500
\thereforeTotal share of
A = 22500 + 5500
= Rs.28,000
Again share of
B = 49,500\times \frac{6}{11}
= 27000
\therefore Hence share of B is Rs 1,000 = [28,000-27,000] less than the share of A.

Short Method :
\because Since A gets 10% of the total profit for looking after the business therefore, B will get the share of profit from 90% of the total point.
\therefore Share of profit B gets
=  55000\times \frac{6}{11}\times \frac{90}{100}
= Rs.27,000
\therefore Share of income A gets
= 55,000 – 27,000
= Rs.28,000
\therefore Required difference
= Rs. (28,000 – 27,000)
= 1000.

Example 2. The partners A, B, C start a business. Twice the investment of A is equal to thrice the capital of B and the capital of B is four times the capital of C. Find the share of each out of a profit of Rs. 2,97, 000.

Solution : Let C’s capital = Rs. x then B’s capital = Rs. 4x
Now, 2 (A,s capital)= 3 (B’s capital)=3\times 4x
\therefore A’s capital= \left ( \frac{3\times 4x}{2} \right ) = 6x
So, ratio of share of A, B and C = 6x : 4x : x = 6 : 4 : 1.
\therefore A’s share =Rs.\left ( 297000\times \frac{6}{11} \right )
= Rs.1,62,000
B’s share of =Rs.\left ( 297000\times \frac{4}{11} \right )
= Rs.108000
and C’s share =Rs.\left ( 297000\times \frac{1}{11} \right )
= Rs.27000.

Example 3: A began a business with Rs. 2100 and is joined afterwards by B with Rs. 3600. After how many months did B join, if the profits at the end of the year are divided equally ?

Solution : Suppose B joines after x months. Then B’s money remained invested for (12-x) months.
\because 2100\times 12= 3600\times (12-x)
\Rightarrow 3600 x = 43200-25200
\therefore x = 18000/3600 = 5
So, B, joined after 5 months.

Example 4: Dilip and Manohar started a business by investing Rs. 1,00,000 and Rs. 1,50,000 respectively. Find the share of each out of profit of Rs. 24,000.

Solution : Ratio of share of Dilip and manohar
= 100000 : 150000 = 2 : 3
\therefore Dilip’s share
= Rs.\left ( 24000\times \frac{2}{5} \right )
= Rs.9600
Manohar’s share
= Rs.\left ( 24000\times \frac{3}{5} \right )
= Rs.14400

Example 5. Sanjay and Raju started a business and invested Rs.20,000 and Rs.25,000 respectively. After 4 months, Raju left Naresh jointed by investing Rs. 15,000. At the end of the year there was a profit of Rs. 4,600. What is the share of Naresh ?

Solution : Ratio of share of Sanjay, Raju and Naresh
= 20,000\times 12 : 25,000\times 4: 15000\times 8
= 12 : 5 : 6:
\therefore share of Naresh
= Rs.\left ( 4600\times \frac{6}{23} \right ) = Rs.1200

 

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