# Partnership Questions and Shortcut Tricks

## 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.
A = $49,500\times \frac{5}{11}$
= Rs.22,500
$\therefore$ Total 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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