CBSE Class 10 Mathematics Partnership, Mixtures and Alligation MCQs Set 08

Mathematics Objective Questions and Answers: Partnership, Mixtures and Alligation

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Multiple Choice Questions

Question 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.
(a) Rs. 16800, 18900, 21000
(b) Rs. 18900, 21000, 16900
(c) Rs. 21000, 18900, 16000
(d) None of these
Show Answer & Explanation

Answer: (a) Rs. 16800, 18900, 21000

Explanation:
1. Ratio of investments = 120 : 135 : 150 = 8 : 9 : 10
2. Shares = 8/27, 9/27 and 10/27 of 56700 = Rs. 16800, 18900 and 21000.

Teacher's Note:
1. With equal time, profit is shared in the ratio of investments.

Question 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 (Alfred, Peter, Ronald).
(a) Rs. 6600, 6600, 3300
(b) Rs. 3300, 6600, 6000
(c) Rs. 6000, 3300, 6600
(d) None of these
Show Answer & Explanation

Answer: (a) Rs. 6600, 6600, 3300

Explanation:
1. Alfred: 45000 × 12 = 540000; Peter: 60000 × 9 = 540000; Ronald: 90000 × 3 = 270000
2. Ratio = 2 : 2 : 1
3. Shares = 2/5, 2/5, 1/5 of 16500 = Rs. 6600, 6600, 3300.

Teacher's Note:
1. Profit is shared in the ratio of (capital × months).

Question 3: A, B and C enter into a partnership. A invests 3 times as much as B invests and B 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?
(a) Rs. 1000
(b) Rs. 2000
(c) Rs. 1200
(d) Rs. 1400
Show Answer & Explanation

Answer: (c) Rs. 1200

Explanation:
1. Let C invest 3k: B = 2k and A = 6k
2. Ratio A : B : C = 6 : 2 : 3
3. B's share = 2/11 × 6600 = Rs. 1200.

Teacher's Note:
1. Express all three investments in terms of one variable.

Question 4: A invested Rs. 76,000 in a business. After a 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?
(a) 4 months
(b) 6 months
(c) 8 months
(d) 3 months
Show Answer & Explanation

Answer: (a) 4 months

Explanation:
1. A: 76000 × 12 and B: 57000 × t, with 76000 × 12 : 57000 × t = 2 : 1
2. 57000 t × 2 = 912000, so t = 8 months
3. B joined after 12 − 8 = 4 months.

Teacher's Note:
1. B's investment lasts for the remaining months only.

Question 5: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio should the profit earned after 2 years be divided between P and Q respectively?
(a) 3 : 4
(b) 3 : 5
(c) 15 : 23
(d) 17 : 3
Show Answer & Explanation

Answer: (d) 17 : 3

Explanation:
1. Both invest for the same period, so the profit ratio equals the investment ratio
2. 85000 : 15000 = 17 : 3.

Teacher's Note:
1. Equal time means the ratio of capitals.

Question 6: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is
(a) Rs. 5400
(b) Rs. 7200
(c) Rs. 8400
(d) Rs. 9600
Show Answer & Explanation

Answer: (c) Rs. 8400

Explanation:
1. Ratio = 22500 : 35000 = 9 : 14
2. Deepak's share = 14/23 × 13800 = Rs. 8400.

Teacher's Note:
1. Simplify the ratio before using it.

Question 7: A, B and C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B and C in an annual profit of Rs. 40,500 are
(a) Rs. 10,500, 13,500, 16,500
(b) Rs. 11,500, 13,000, 16,000
(c) Rs. 11,000, 14,000, 15,500
(d) Rs. 11,500, 12,500, 16,500
Show Answer & Explanation

Answer: (a) Rs. 10,500, 13,500, 16,500

Explanation:
1. Ratio = 35 : 45 : 55 = 7 : 9 : 11 (total 27)
2. Shares = 7/27, 9/27, 11/27 of 40500 = Rs. 10500, 13500, 16500.

Teacher's Note:
1. One part = 40500/27 = Rs. 1500.

Question 8: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
(a) Rs. 9423
(b) Rs. 10,250
(c) Rs. 12,500
(d) Rs. 10,500
Show Answer & Explanation

Answer: (d) Rs. 10,500

Explanation:
1. Simran: 50000 × 36 = 1800000; Nanda: 80000 × 30 = 2400000; ratio = 3 : 4
2. Simran's share = 3/7 × 24500 = Rs. 10500.

Teacher's Note:
1. Convert 3 years to 36 months.

Question 9: A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the start of the business?
(a) Rs. 7500
(b) Rs. 9000
(c) Rs. 9500
(d) Rs. 10,000
Show Answer & Explanation

Answer: (a) Rs. 7500

Explanation:
1. A: 20000 × 24 = 480000; B: 15000 × 24 = 360000; C: 20000 × 18 = 360000
2. Ratio = 4 : 3 : 3
3. B's share = 3/10 × 25000 = Rs. 7500.

Teacher's Note:
1. C invests for 18 months.

Question 10: A, B and C invested Rs. 1260, Rs. 840 and Rs. 2100 respectively in a partnership business. The share of C in a total profit of Rs. 2420 is
(a) Rs. 726
(b) Rs. 484
(c) Rs. 1210
(d) Rs. 1110
Show Answer & Explanation

Answer: (c) Rs. 1210

Explanation:
1. Ratio = 1260 : 840 : 2100 = 3 : 2 : 5
2. C's share = 5/10 × 2420 = Rs. 1210.

Teacher's Note:
1. Divide by the common factor 420.

Question 11: In a business A invested Rs. 2000 for 6 months, B invested Rs. 4000 for 3 months and C invested Rs. 3000 for 4 months. They divide a profit of Rs. 3300 in the ratio of their investments. The share of A is
(a) Rs. 3600
(b) Rs. 800
(c) Rs. 1000
(d) Rs. 1100
Show Answer & Explanation

Answer: (d) Rs. 1100

Explanation:
1. A: 2000 × 6 = 12000; B: 4000 × 3 = 12000; C: 3000 × 4 = 12000
2. The ratio is 1 : 1 : 1, so A's share = 3300/3 = Rs. 1100.

Teacher's Note:
1. Capital × time is the same for all three.

Question 12: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is
(a) Rs. 1425
(b) Rs. 1500
(c) Rs. 1537.50
(d) Rs. 1576
Show Answer & Explanation

Answer: (b) Rs. 1500

Explanation:
1. After charity, 95% of the profit is shared, A getting 3/5 of it
2. 0.95 × 3/5 × T = 855, so 0.57 T = 855 and T = Rs. 1500.

Teacher's Note:
1. Charity is deducted before sharing.

Question 13: Avinash invested an amount of Rs. 25,000 and started a business. Jitendra joined him after one year with an amount of Rs. 30,000. After two years from starting the business they earned a profit of Rs. 46,000. What will be Jitendra's share in the profit?
(a) Rs. 14,000
(b) Rs. 12,000
(c) Rs. 16,000
(d) Rs. 17,250
Show Answer & Explanation

Answer: (d) Rs. 17,250

Explanation:
1. Avinash: 25000 × 24 = 600000; Jitendra: 30000 × 12 = 360000
2. Ratio = 5 : 3
3. Jitendra's share = 3/8 × 46000 = Rs. 17250.

Teacher's Note:
1. Jitendra's money works for one year only.

Question 14: A invests Rs. 3000 for one year in a business. How much should B invest in order that the profit after 1 year may be divided in the ratio of 2 : 3?
(a) Rs. 2000
(b) Rs. 1800
(c) Rs. 3600
(d) Rs. 4500
Show Answer & Explanation

Answer: (d) Rs. 4500

Explanation:
1. With equal time, the profit ratio equals the investment ratio
2. 3000 : x = 2 : 3, so x = 3000 × 3/2 = Rs. 4500.

Teacher's Note:
1. The ratio of investments equals the ratio of profits for equal time.

Question 15: Prabodh bought 30 kg of rice at the rate of Rs. 8.50 per kg and 20 kg of rice at the rate of Rs. 9.00 per kg. He mixed the two. At what price (approx.) per kg should he sell the mixture in order to get 20% profit?
(a) Rs. 9.50
(b) Rs. 12.50
(c) Rs. 10.50
(d) Rs. 12.00
Show Answer & Explanation

Answer: (c) Rs. 10.50

Explanation:
1. Total cost = 255 + 180 = Rs. 435 for 50 kg, so average cost = Rs. 8.70 per kg
2. SP = 8.70 × 1.2 = Rs. 10.44, approximately Rs. 10.50.

Teacher's Note:
1. Find the cost of the whole mixture first.

Question 16: Prabhu purchased 30 kg of rice at the rate of Rs. 17.50 per kg and another 30 kg of rice at a certain rate. He mixed the two and sold the entire quantity at the rate of Rs. 18.60 per kg and made 20 percent overall profit. At what price per kg did he purchase the lot of another 30 kg rice?
(a) Rs. 14.50
(b) Rs. 12.50
(c) Rs. 15.50
(d) Rs. 13.50
Show Answer & Explanation

Answer: (d) Rs. 13.50

Explanation:
1. Total SP = 60 × 18.60 = Rs. 1116
2. Total cost = 1116/1.2 = Rs. 930
3. Cost of the second lot = 930 − 525 = Rs. 405, so rate = 405/30 = Rs. 13.50 per kg.

Teacher's Note:
1. Work back from the selling price to the total cost.

Question 17: A, B and C are partners of a company. During a particular year A received one-third of the profit, B received one-fourth of the profit and C received the remaining Rs. 5,000. How much did A receive?
(a) Rs. 5,000
(b) Rs. 4,000
(c) Rs. 3,000
(d) Rs. 1,000
Show Answer & Explanation

Answer: (b) Rs. 4,000

Explanation:
1. C's share = 1 − 1/3 − 1/4 = 5/12 of the profit = 5000
2. Total profit = Rs. 12000, so A's share = 1/3 × 12000 = Rs. 4000.

Teacher's Note:
1. Add the fractions before finding the remainder.

Question 18: Nikita bought 30 kg of wheat at the rate of Rs. 4.75 per kg, 40 kg of wheat at Rs. 4.25 per kg and mixed them. She sold the mixture at the rate of Rs. 4.45 per kg. Her total profit or loss in the transaction was
(a) Rs. 1 loss
(b) Rs. 1 profit
(c) Rs. 3.50 loss
(d) Rs. 3.50 profit
Show Answer & Explanation

Answer: (a) Rs. 1 loss

Explanation:
1. Cost = 30 × 4.75 + 40 × 4.25 = 142.50 + 170 = Rs. 312.50
2. SP = 70 × 4.45 = Rs. 311.50
3. Loss = Rs. 1.

Teacher's Note:
1. Compare total cost with total selling price.

Question 19: A mixture contains spirit and water in the ratio 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is
(a) 10 litres
(b) 12 litres
(c) 8 litres
(d) 9 litres
Show Answer & Explanation

Answer: (d) 9 litres

Explanation:
1. The difference of 1 part is 3 litres
2. Spirit = 3 parts = 9 litres.

Teacher's Note:
1. The ratio terms differ by 1 part.

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