**Q1. Vinod and Ankit started a business by investing capitals in the ratio of 2:3. If Vinod had invested an additional amount of Rs. 10000, the ratio of Vinod’s investment to Ankit’s investment would have been 3:2. What was the amount invested by Vinod initially?**

(a) Rs. 8000

(b) Rs. 12000

(c) Rs. 9000

(d) Data inadequate

**Q2. Mr. Saxena started a business by investing Rs. 5000. Four months later, Mr. Jain joined the business by investing Rs. 9000. If the profit at the end of the year was Rs. 22000, then how much amount would Mr. Jain have received as the profit?**

(a) Rs. 16000

(b) Rs. 14000

(c) Rs. 12000

(d) Rs. 11000

**Q3. Rs.700 is divided among A, B and C so that A receives half as much as B and B half as much as C. Then C’s share is:**

A. Rs.200

B. Rs.300

C. Rs.400

D. Rs.600

**Q4. A started a business with Rs. 10000. B joined him later with a capital of Rs. 40000. If at the end of the year, they both received equal shares of the profit. How many months after the business started did B join it?**

(a) 4 months

(b) 6 months

(c) 8 months

(d) 9 months

**Q5. A starts business with Rs. 3500. 5 months later B joins A as his partner. After a year, the profit is divided in the ratio of 2:3. What is B’s contribution in the capital?**

(a) Rs. 8000

(b) Rs. 8500

(c) Rs. 9000

(d) Rs. 7500

**Q6. Vinay started a business investing Rs. 70000. Ashok joined him after six months with an amount of Rs. 105000. Sunil joined them with Rs. 1.4 Lakh after another six months. The amount of profit earned should be distributed in what ratio among Vinay, Ashok and Sunil, three years after Vinay started the business?**

(a) 42:45:56

(b) 7:6:10

(c) 12:15:16

(d) None of these

**Q7. Veena started a business, investing Rs. 75000. After 3 months, Poonam joined her with an amount of Rs. 125000 and after another six months Sarita joined them with an amount of Rs. 150000. Profit earned at the end of three years from when Veena started the business should be distributed in what ratio among Veena, Poonam and Sarita, respectively?**

(a) 36:55:54

(b) 18:28:27

(c) 35:54:55

(d) 35:54:57

**Q8. A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, then how much C must pay as his share of rent?**

(a) Rs. 45

(b) Rs. 50

(c) Rs. 55

(d) Rs. 60

**Q9. Arun started a business investing Rs. 38000. After 5 months Bakul joined him with a capital of Rs. 55000. At the end of the year the total profit was Rs. 22000. What is the approximate difference between the share of profits of Arun and Bakul?**

(a) Rs. 1192

(b) Rs. 1856

(c) Rs. 1007

(d) Rs. 1928

**Q10. In a business B a sleeping partner and A is a working partner. A invests Rs. 5000 and B invests 6000. A receives 25/2%**

**of profit for managing the business and the remaining amount is divided in proportion to their capitals. A’s share of profit in a profit of Rs. 880 is:**

(a) Rs. 350

(b) Rs. 400

(c) Rs. 420

(d) Rs. 460

**Solutions**

S1. Ans.(a)

Sol. Let the initial investments of Vinod and Ankit be 2x and 3x, respectively.

As per the question,

(2x+ 10000)/3x = 3/2

4x + 20000 = 9x

∴ x = 4000

∴ Amount invested by Vinod = 2x = Rs. 8000.

S2. Ans.(c)

Sol. Ratio of their investments

= 50000 × 12: 90000 × 8 = 5: 6

∴ Amount received by Mr Jain

= (6/11) × 22000 = Rs. 12000.

S3. Ans.(C)

Let C’s share = Rs. x. Then

B’s share = Rs. x/2

And, A’s share = Rs. x/4

A: B:C = x/4:x/2:x=1:2:4

Hence, C’s share = Rs. (700)×(4/7) = Rs.400

S4. Ans.(d)

Sol. Suppose, B joins A after K months.

∴ Investments of A and B are in the ratio of

10000 × 12: 40000 × (12 – K) = 1:1

∴ 10000 × 12 = 40000 × (12 – K)

i.e, 4(12 – K) = 12 ⇒ K = 9.

S5. Ans.(c)

Sol. Let, B’s contribution be Rs. x

∴ (3500×12)/7x = 2/3

or, x=(3500 × 12 × 3)/(7 × 2)

∴x = 9000.

S6. Ans.(c)

Sol. Ratio of their investments

= 70 × 36: 105 × 30: 140 × 24

= 12: 15: 16.

S7. Ans.(a)

Sol. Ratio of their profits

= 75 × 36: 125 × 33: 150 × 27

= 3 × 36: 5 × 33: 6 × 27

= 3 × 12: 5 × 11: 6 × 9

= 36:55:54.

S8. Ans.(a)

Sol. A, B and C pay in the ratio of

10 × 7 : 12 × 5 : 15 × 3

i.e., 70:60:45

i.e., 14:12:9

∴ C pay Rs. (9/35) × 175 = Rs. 45.

S9. Ans.(b)

Sol. Ratio of investment of Arun: Bakul

= 38000 × 12: 55000 × 7 = 38 × 12 : 55 × 7

= 456:385 ≈ 45:38

Required difference = (22000/(45 + 38)) × (45 – 38)

=(22000 × 7)/83 ≈ 22000/12 ≈ 1835 ≈ Rs. 1856.

S10. Ans.(d)

Sol. A’s share for managing the business

= 12 1/2% of Rs. 880 = Rs. 110

Remaining profit = Rs. 770

Profit ratio of A and B = 5:6

A’s share = 5/11 of Rs. 770 = Rs. 350.

A’s total profit = Rs. 350 + Rs. 110 = Rs. 460.

Sol. Let the initial investments of Vinod and Ankit be 2x and 3x, respectively.

As per the question,

(2x+ 10000)/3x = 3/2

4x + 20000 = 9x

∴ x = 4000

∴ Amount invested by Vinod = 2x = Rs. 8000.

S2. Ans.(c)

Sol. Ratio of their investments

= 50000 × 12: 90000 × 8 = 5: 6

∴ Amount received by Mr Jain

= (6/11) × 22000 = Rs. 12000.

S3. Ans.(C)

Let C’s share = Rs. x. Then

B’s share = Rs. x/2

And, A’s share = Rs. x/4

A: B:C = x/4:x/2:x=1:2:4

Hence, C’s share = Rs. (700)×(4/7) = Rs.400

S4. Ans.(d)

Sol. Suppose, B joins A after K months.

∴ Investments of A and B are in the ratio of

10000 × 12: 40000 × (12 – K) = 1:1

∴ 10000 × 12 = 40000 × (12 – K)

i.e, 4(12 – K) = 12 ⇒ K = 9.

S5. Ans.(c)

Sol. Let, B’s contribution be Rs. x

∴ (3500×12)/7x = 2/3

or, x=(3500 × 12 × 3)/(7 × 2)

∴x = 9000.

S6. Ans.(c)

Sol. Ratio of their investments

= 70 × 36: 105 × 30: 140 × 24

= 12: 15: 16.

S7. Ans.(a)

Sol. Ratio of their profits

= 75 × 36: 125 × 33: 150 × 27

= 3 × 36: 5 × 33: 6 × 27

= 3 × 12: 5 × 11: 6 × 9

= 36:55:54.

S8. Ans.(a)

Sol. A, B and C pay in the ratio of

10 × 7 : 12 × 5 : 15 × 3

i.e., 70:60:45

i.e., 14:12:9

∴ C pay Rs. (9/35) × 175 = Rs. 45.

S9. Ans.(b)

Sol. Ratio of investment of Arun: Bakul

= 38000 × 12: 55000 × 7 = 38 × 12 : 55 × 7

= 456:385 ≈ 45:38

Required difference = (22000/(45 + 38)) × (45 – 38)

=(22000 × 7)/83 ≈ 22000/12 ≈ 1835 ≈ Rs. 1856.

S10. Ans.(d)

Sol. A’s share for managing the business

= 12 1/2% of Rs. 880 = Rs. 110

Remaining profit = Rs. 770

Profit ratio of A and B = 5:6

A’s share = 5/11 of Rs. 770 = Rs. 350.

A’s total profit = Rs. 350 + Rs. 110 = Rs. 460.