Arithmetic aptitude :: Partnership :: General

• Partnership - General
• Partnership - Data Sufficiency 1
• Partnership - Data Sufficiency 2
• Partnership - Data Sufficiency 3
• Partnership - Important Formulas and Facts

Partnership:

When two or more people runs a joint business, they are called partners and the deal is known as partnership.

Ratio of Divisions of Gains

If two partners, $A$ and $B$ invest Rs. $x$ and Rs. $y$ respectively for a year in a business, then at the end of the year:
($A$'s share of profit) : ($B$'s share of profit) $=x:y$.

If $A$ invests Rs. $x$ for $p$ months and $B$ invests Rs. $y$ for $q$ months then,
($A$'s share of profit) : ($B$'s share of profit) $=xp:yq$.

Working and Sleeping Partners:

working partner is the one who runs the business and sleeping partner is the one who simply invests the money in the business.

A invested Rs. 76,000 in a business. After few months, B joined him with Rs. 57,000. At the end of the year, the total profit was divided between them in the ratio 2 : 1. After how many months did B join ?

Answer:

Explanation:

Suppose $B$ joined after $x$ months.

Then, B's money was invested for $(12-x)$ months.

$\frac{76000\times12}{57000\times(12-x)}$ $ =\frac{2}{1}$

$\Leftrightarrow 912000$ $=114000(12-x)$

$\Leftrightarrow 114(12-x)$ $=912$ $\Leftrightarrow (12-x)=8$  

$\Leftrightarrow x = 4$.

Hence, B joined after 4 months.

Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 cows for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 720, find the total rent of the field.

Answer:

Explanation:

Ratio of shares of $A$, $B$, $C$, $D$ $=(24\times 3)$ $:(10\times 5)$ $:(35\times 4)$ $:(21\times 3)$

$=72:50:140:63$.

Let total rent be Rs. $x$.

Then, A's share = Rs. $\frac{72x}{325}$.

$\frac{72x}{325}$ $= 720$.

$x=\frac{720\times 325}{72}$ $= 3250$.

Hence, total rent of the field is Rs. 3250.

A, B and C enter into partnership. A invests 3 times as much as B invests and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B ?

Answer:

Explanation:

Let C's capital = Rs. $x$.

Then, B's capital = Rs. $\frac{2}{3}x.$

A's capital = Rs. $\left(3\times\frac{2}{3}x\right)$ $=Rs.2x$.

Ratio of their capitals $=2x:\frac{2}{3}x:x$ $= 6:2:3$.

Hence, B's share = Rs. $\left(6600\times\frac{2}{11}\right)$ = Rs. 1200.

A, B and C start a business each investing Rs. 20,000. After 5 months A withdrew Rs. 5000, B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.

Answer:

Explanation:

Ratio of the capitals of $A$, $B$ and $C$

$=20000\times 5+15000\times 7$ $:20000\times 5+16000\times 7$ $:20000\times 5+26000\times 7$

$=205000:212000:282000$

$=205:212:282$.

A's share = Rs. $\left(69900\times\frac{205}{699}\right)$ = Rs. 20500.

B's share = Rs. $\left(69900\times\frac{212}{699}\right)$  = Rs. 21200.

C's share = Rs $\left(69900\times\frac{282}{699}\right)$  = Rs. 28200.

Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital ofRs. 90,000. At the end of the year, they made a profit ofRs. 16,500. Find the share of each.

Answer:

Explanation:

Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald for 3 months.

So, ratio of their capitals $=(45000\times 12)$ $:(60000\times 9)$ $:(90000\times 3)$

$=540000:540000:270000$ $= 2:2:1$.

Alfred's share = Rs. $\left(16500\times\frac{2}{5}\right)$ = Rs. 6600.

Peter's share = Rs. $\left(16500\times\frac{2}{5}\right)$ = Rs. 6600.

Ronald's share = Rs. $\left(16500\times\frac{1}{5}\right)$ = Rs. 3300.

• Partnership - General
• Partnership - Data Sufficiency 1
• Partnership - Data Sufficiency 2
• Partnership - Data Sufficiency 3