Partnership problems with solution - part 1

Introduction

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Solved Problems

1. A, B, and C started a business each investing Rs.10000. After 4 month A withdraws Rs.3000, B withdraws Rs.4000, and C invests Rs.3000 more. At the end of the year, the total profit was Rs.32800. Find the share of C.

Answer: 14400

Explanation:

Ratio of the capital of A, B, and C.

= ( 10,000 × 4 + 7000 × 8 ) : ( 10,000 × 4 + 6000 × 8 ) : ( 10,000 × 4 + 13000 x 8 )

= 96000 : 88000 : 144000

So, Ratio becomes 12 : 11 : 18

= 32800 × 18/41

= 14400

Distributing the final profit of Rs. 32800 in the given ratio, the share of C becomes 14400.

2. Divide Rs. 100 among three people so that the second will have twice as much as the first, and the third will have Rs. 5 less than the second. How much does each people receive?

Answer: Rs. 21, Rs. 42 and Rs. 37

Explanation:

Let First people share = Rs. x

Second people share = Rs. 2x

Third people share = Rs. 2x - 5

Total amount = Rs. 100

( x + 2x + 2x - 5 ) = 100

3x + 2x - 5 =100

5x - 5 =100

5x = 100 + 5

x = 105 / 5

x = Rs. 21

Second people share = Rs. 2x

= ( 2 × 21 )

= Rs. 42

Third people share = Rs. 2x - 5

= ( 42 - 5 )

= Rs. 37

Each people will receive Rs. 21, Rs. 42 and Rs. 37 respectively.

3. Shakeel started a software business by investing Rs. 20,000. After six months, Neel joined him with a capital of Rs. 30,000. After 3 years, they earned a profit of Rs. 13,950. What was Shakeel's share in the profit?

Answer: Rs. 6200

Explanation

Ratio of capitals of Shakeel and Neel

= (20,000 × 36) : (30,000 × 30) = 720000: 900000

= 4 : 5

Shakeel's share = Rs. 13950 × 4 / 9

Shakeel's share = Rs. 6200

4. A, B, and C started a business by investing Rs. 250000, Rs. 300000, and Rs.350000 respectively. Find the share of B, out of an annual profit of Rs.187200.

Answer: Rs. 62400

Explanation

Ratio of shares of A, B and C = Ratio of their investment A : B : C

= 250000 : 300000 : 350000 = 5 : 6 : 7

Share of B = Rs. [187200 × ( 6 / 18 )]

Share of B = Rs. 62400

5. A started a business with Rs. 18,000 and is joined afterward by B with Rs. 54,000. After how many months did B join if the profits at the end of the year are divided equally?

Answer: 8

Explanation:

Given data,

A's Investment = Rs. 18000

B's Investment = Rs. 54000

Let the duration of B's capital was used be x months Investment × duration = Profit Then,

18000 × 12 = 54000 × ( 12 - x )

( 18000 × 12 ) / 54000 = 12 - x

4 = 12 - x

x = 12 - 4

x = 8

B will join if the profits at the end of the year are divided equally is after 8 months.

Conclusion

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