Partnership Problems with Solutions for SSC and Bank Exams

Partnership Problems with Solutions for Competitive Exams

Q.1. A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 and Rs. 1,50,000 respectively. Find the share of each, out of an annual profit of Rs. 56,700.

Solution:

Ratio of shares of A,B and C = Ratio of their investments

                                                   = 120000 : 135000  :  150000 = 8 : 9 : 10.

$$ ∴ A's \ share = Rs. \left(56700×{8\over27}\right)= Rs. 16800.$$

   $$  B's \  share = Rs. \left(56700×{9\over27}\right)= Rs. 18900.$$

   $$  C's \ share = Rs. \left(56700×{10\over27}\right)= Rs.21000.$$

Q.2. 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 of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the share of each.

Solution: 

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

So ratio of their capitals = (45000×12) : (60000×9) : (90000×3)

                                            = 540000 : 540000 : 270000 = 2 : 2 : 1

$$ ∴ Alfred's\ share = Rs. \left(16500×{2\over5}\right)= Rs.6600;$$

   $$  Peter's \   share = Rs. \left(16500×{2\over5}\right)= Rs. 6600;$$

   $$  Ronald's \   share = Rs. \left(16500×{1\over5}\right)= Rs.3300;$$

Q.3. 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. 

Solution: 

Ratio of the capitals of A, B and C

= 20000×5+15000×7 : 20000×5+16000×7: 20000×5+26000×7

= 205000 : 212000 : 282000 = 205 : 212 : 282.

$$ ∴ A's\ share = Rs. \left(69900×{205\over699}\right)= Rs.20500;$$

  $$  B's \  share = Rs. \left(69900×{212\over699}\right)= Rs. 21200;$$

  $$  C's \  share = Rs. \left(69900×{282\over699}\right)= Rs.28200;$$

Q.4. A, B and C enter into partnership. A invests 3 times as much as B invests and invests two-thirds of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B?

Solution:

Let C’s capital = Rs. x. Then, B, capital = Rs.

$$  A's\ capital = Rs. \left(3×{2\over3}x\right)= Rs.2x.$$

  $$= 2x : {2\over3}x:x=6:2:3. $$

  $$ Hence, B's \ share = Rs.\left(6000×{2\over11}\right)=Rs.1200.$$

Q.5. Four milkman 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.

Solution:

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

                                                   = 72 : 50 : 140 : 63.

Let total rent be Rs. x. Then, A’s share = Rs. .

$$ ∴  {72x\over325}=720↔x={720×325\over72}=3250$$

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

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