CBSE Class 10 Mathematics Commercial Mathematics MCQs Set 27

Mathematics Objective Questions and Answers: Commercial Mathematics

Access targeted multiple-choice questions for Commercial Mathematics designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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View or download the dedicated Commercial Mathematics MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: Arun purchased 30 kg of wheat at Rs. 11.50 per kg and 20 kg of wheat at Rs. 14.25 per kg. He mixed the two. Approximately what price per kg should he sell the mixture at to make a 30% profit?
(a) Rs. 14.80
(b) Rs. 15.40
(c) Rs. 15.60
(d) Rs. 16.30
Show Answer & Explanation

Answer: (d) Rs. 16.30

Explanation:
1. Total cost = 345 + 285 = Rs. 630 for 50 kg, so cost = Rs. 12.60 per kg.
2. Selling price = 1.3 × 12.60 = Rs. 16.38, which is approximately Rs. 16.30.

Teacher's Note:
1. Find the average cost of the mixture before adding the profit.

Question 2: Padam purchased 30 kg of rice at 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 Rs. 18.60 per kg, making a 20% overall profit. At what price per kg did he purchase the second lot?
(a) Rs. 12.50
(b) Rs. 13.50
(c) Rs. 14.50
(d) Rs. 15.50
Show Answer & Explanation

Answer: (b) Rs. 13.50

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

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

Question 3: How many kg of wheat costing Rs. 8 per kg must be mixed with 36 kg of rice costing Rs. 5.40 per kg so that a 20% gain is obtained by selling the mixture at Rs. 7.20 per kg?
(a) 10.08 kg
(b) 8.6 kg
(c) 9.2 kg
(d) 10.8 kg
Show Answer & Explanation

Answer: (d) 10.8 kg

Explanation:
1. Cost price of the mixture = 7.20/1.2 = Rs. 6 per kg.
2. Let x kg of wheat be added: 8x + 194.4 = 6(x + 36), so 2x = 21.6 and x = 10.8 kg.

Teacher's Note:
1. Convert the selling price to the cost price of the mixture first.

Question 4: In what ratio must water be mixed with milk costing Rs. 12 per litre to obtain a mixture worth Rs. 8 per litre?
(a) 1 : 2
(b) 2 : 1
(c) 2 : 3
(d) 3 : 2
Show Answer & Explanation

Answer: (a) 1 : 2

Explanation:
1. Let water : milk = w : m. Cost of mixture: 12m/(w + m) = 8, so 12m = 8w + 8m.
2. 4m = 8w, so w : m = 1 : 2.

Teacher's Note:
1. Water has zero cost.

Question 5: An amount of Rs. 2430 is divided among A, B and C such that if their shares are reduced by Rs. 5, Rs. 10 and Rs. 15 respectively, the remainders are in the ratio 3 : 4 : 5. B's share was
(a) Rs. 605
(b) Rs. 790
(c) Rs. 800
(d) Rs. 810
Show Answer & Explanation

Answer: (d) Rs. 810

Explanation:
1. After the reductions the total is 2430 − 30 = Rs. 2400, so one part = 2400/12 = 200.
2. B's remainder is 800, so B's share = 800 + 10 = Rs. 810.

Teacher's Note:
1. Do not forget to add back the amount deducted.

Question 6: A sum of Rs. 53 is divided among A, B and C such that A gets Rs. 7 more than B and B gets Rs. 8 more than C. The ratio of their shares is
(a) 16 : 9 : 18
(b) 25 : 18 : 10
(c) 18 : 25 : 10
(d) 15 : 8 : 30
Show Answer & Explanation

Answer: (b) 25 : 18 : 10

Explanation:
1. Let C get x. Then B = x + 8 and A = x + 15.
2. 3x + 23 = 53 gives x = 10, so the shares are 25, 18, 10.

Teacher's Note:
1. Express all shares in terms of the smallest.

Question 7: A, B and C enter into partnership. A invests 3 times as much as B and B invests two-thirds of what C invests. At the end of the year the profit is Rs. 6600. The share of B is
(a) Rs. 3600
(b) Rs. 1800
(c) Rs. 1200
(d) None of these
Show Answer & Explanation

Answer: (c) Rs. 1200

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

Teacher's Note:
1. Fix one investment and express the others as multiples.

Question 8: Simran started a business by investing Rs. 50,000. After six months Nanda joined her with Rs. 80,000. After 3 years they earned a profit of Rs. 24,500. Simran's share of the profit was
(a) Rs. 9423
(b) Rs. 10,500
(c) Rs. 12,500
(d) Rs. 14,000
Show Answer & Explanation

Answer: (b) Rs. 10,500

Explanation:
1. Simran: 50000 × 36 and Nanda: 80000 × 30, a ratio of 3 : 4.
2. Simran's share = 3/7 × 24500 = Rs. 10,500.

Teacher's Note:
1. Count the months each partner's money was invested.

Question 9: A, B and C invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year B withdraws Rs. 40,000 and C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
(a) 2 : 3 : 5
(b) 3 : 4 : 7
(c) 4 : 5 : 9
(d) None of these
Show Answer & Explanation

Answer: (d) None of these

Explanation:
1. A: 40000 × 36 = 1440000 (in thousands: 1440).
2. B: 80 × 12 + 40 × 24 = 1920. C: 120 × 12 + 40 × 24 = 2400.
3. Ratio = 1440 : 1920 : 2400 = 3 : 4 : 5, which is not among (a) to (c).

Teacher's Note:
1. Split each investment into the periods before and after the withdrawal.

Question 10: A invests some money at the beginning, B invests double the amount after 6 months and C invests thrice the amount after 8 months. If the annual profit is Rs. 27,000, C's share is
(a) Rs. 8625
(b) Rs. 9000
(c) Rs. 10,800
(d) Rs. 11,250
Show Answer & Explanation

Answer: (b) Rs. 9000

Explanation:
1. A: x × 12, B: 2x × 6, C: 3x × 4, all equal 12x.
2. The profit is shared equally: 27000/3 = Rs. 9000.

Teacher's Note:
1. Compute capital times months for each partner.

Question 11: In a business, A and C invested amounts in the ratio 2 : 1, while the ratio between the amounts invested by A and B was 3 : 2. If the profit was Rs. 1,57,300, how much did B receive?
(a) Rs. 24,200
(b) Rs. 36,300
(c) Rs. 48,400
(d) Rs. 72,600
Show Answer & Explanation

Answer: (c) Rs. 48,400

Explanation:
1. A : B : C = 6 : 4 : 3, a total of 13 parts.
2. B = 4/13 × 157300 = Rs. 48,400.

Teacher's Note:
1. Combine the two ratios using the common term A.

Question 12: A, B and C start a business with investments in the ratio 1 : 3 : 5. After 4 months A invests the same additional amount as before, while B and C withdraw half of their investments. The ratio of their profits at the end of the year is
(a) 4 : 3 : 5
(b) 5 : 6 : 10
(c) 6 : 5 : 10
(d) 10 : 5 : 6
Show Answer & Explanation

Answer: (b) 5 : 6 : 10

Explanation:
1. A: 1 × 4 + 2 × 8 = 20. B: 3 × 4 + 1.5 × 8 = 24. C: 5 × 4 + 2.5 × 8 = 40.
2. Ratio 20 : 24 : 40 = 5 : 6 : 10.

Teacher's Note:
1. Add the capital-months of the two periods.

Question 13: A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. The gain at the end of 10 months was Rs. 760. A's share is
(a) Rs. 330
(b) Rs. 360
(c) Rs. 380
(d) Rs. 430
Show Answer & Explanation

Answer: (a) Rs. 330

Explanation:
1. A: 4 × 3 + 3 × 7 = 33. B: 5 × 3 + 4 × 7 = 43.
2. A's share = 33/76 × 760 = Rs. 330.

Teacher's Note:
1. After the withdrawal A has 3/4 of 4 = 3 units and B has 4/5 of 5 = 4 units.

Question 14: A starts a business with Rs. 3500 and after 5 months B joins as his partner. After a year the profit is divided in the ratio 2 : 3. B's contribution to the capital is
(a) Rs. 7500
(b) Rs. 8000
(c) Rs. 8500
(d) Rs. 9000
Show Answer & Explanation

Answer: (d) Rs. 9000

Explanation:
1. A: 3500 × 12 = 42000. B: x × 7.
2. 42000 : 7x = 2 : 3, so 14x = 126000 and x = Rs. 9000.

Teacher's Note:
1. B's money works for 7 months.

Question 15: A tin of oil was 4/5 full. When six bottles of oil were taken out and four bottles were poured in, it was 3/4 full. What is the capacity of the tin in bottles?
(a) 16
(b) 40
(c) 32
(d) None of these
Show Answer & Explanation

Answer: (b) 40

Explanation:
1. Let the capacity be N bottles: 4N/5 − 6 + 4 = 3N/4.
2. N/20 = 2, so N = 40 bottles.

Teacher's Note:
1. Net removal is 2 bottles, which is the difference between 4/5 and 3/4 of the capacity.

Question 16: If 5 men can cane 5 chairs in 5 hours, then in how many hours will 1 man cane 1 chair?
(a) 1 hour
(b) 15 hours
(c) 5 hours
(d) 10 hours
Show Answer & Explanation

Answer: (c) 5 hours

Explanation:
1. One man caning one chair is the same ratio of men to chairs, so the time is unchanged: 5 hours.

Teacher's Note:
1. Work is proportional to men x time.

Question 17: If 4 workers can dig a 20 m long ditch in 6 days, find the length dug by 2 workers in a day (in metres).
(a) 1 2/3
(b) 3 2/4
(c) 3 2/3
(d) 1 3/2
Show Answer & Explanation

Answer: (a) 1 2/3

Explanation:
1. One worker in one day digs 20/(4 × 6) = 5/6 m.
2. Two workers dig 5/3 = 1 2/3 m in a day.

Teacher's Note:
1. Find the work of one worker in one day.

Question 18: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B now works at half his usual rate (half a day daily), in how many days will A and B together complete the work?
(a) 15 days
(b) 20 days
(c) 45 days
(d) 30 days
Show Answer & Explanation

Answer: (a) 15 days

Explanation:
1. B alone takes 30 days, since 1/12 − 1/20 = 1/30.
2. Rate now = 1/20 + 1/60 = 1/15, so 15 days.

Teacher's Note:
1. Halving the daily hours halves B's rate.

Question 19: Harpal is thrice as good a workman as Kewal and takes 10 days less to do a piece of work than Kewal takes. Kewal can do that work in
(a) 8 days
(b) 12 days
(c) 13 days
(d) 15 days
Show Answer & Explanation

Answer: (d) 15 days

Explanation:
1. If Harpal takes t days, Kewal takes 3t days and 3t − t = 10, so t = 5.
2. Kewal takes 15 days.

Teacher's Note:
1. Efficiency and time are inversely proportional.

Question 20: A takes 10 days less than the time taken by B to finish a piece of work. If A and B together can finish the work in 12 days, the time taken by B alone is
(a) 20 days
(b) 30 days
(c) 40 days
(d) 50 days
Show Answer & Explanation

Answer: (b) 30 days

Explanation:
1. 1/(x − 10) + 1/x = 1/12 gives x² − 34x + 120 = 0.
2. x = 30 or 4; since A's time x − 10 must be positive, x = 30 days.

Teacher's Note:
1. Reject the root that gives a negative time.

Question 21: A, B and C can complete a work working alone in 10, 15 and 20 days respectively. If all of them work together to complete the work, what fraction of the work is done by B?
(a) 4/13
(b) 1/2
(c) 1/3
(d) 6/13
Show Answer & Explanation

Answer: (a) 4/13

Explanation:
1. Efficiencies are in the ratio 1/10 : 1/15 : 1/20 = 6 : 4 : 3.
2. B does 4/13 of the work.

Teacher's Note:
1. Work done is proportional to efficiency when everyone works for the same time.

Question 22: A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it working together 42/5 hours a day?
(a) 3 days
(b) 4 days
(c) 4.5 days
(d) None of these
Show Answer & Explanation

Answer: (a) 3 days

Explanation:
1. A needs 63 hours and B needs 42 hours, so together they need 126/5 = 25.2 hours.
2. 25.2 ÷ 8.4 = 3 days.

Teacher's Note:
1. Convert both to hours of work.

Question 23: A can do a piece of work in 24 days. If B is 60% more efficient than A, the number of days B needs to do twice as large a work is
(a) 24
(b) 36
(c) 15
(d) 30
Show Answer & Explanation

Answer: (d) 30

Explanation:
1. B alone takes 24/1.6 = 15 days for the original work.
2. Twice the work takes 30 days.

Teacher's Note:
1. Time is inversely proportional to efficiency.

Question 24: A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is
(a) 4 days
(b) 6 days
(c) 8 days
(d) 18 days
Show Answer & Explanation

Answer: (a) 4 days

Explanation:
1. A takes 6 days. Together: 1/6 + 1/12 = 1/4.
2. They finish in 4 days.

Teacher's Note:
1. Add the daily rates.

Question 25: Taps A and B can fill a tank in 12 minutes and 15 minutes respectively. Both are opened and after 3 minutes A is closed. How much longer does B take to fill the rest of the tank?
(a) 7 min 45 sec
(b) 7 min 15 sec
(c) 8 min 5 sec
(d) 8 min 15 sec
Show Answer & Explanation

Answer: (d) 8 min 15 sec

Explanation:
1. In 3 minutes the two fill 3 × (1/12 + 1/15) = 27/60 of the tank.
2. The remaining 33/60 is filled by B in 33/60 × 15 = 8.25 min = 8 min 15 sec.

Teacher's Note:
1. Subtract what has already been filled.

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FAQs

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