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Arithmetic MCQ with Answers

20 questionswith explanationsfor RAS, Patwari, VDO and other Rajasthan exams

Questions

Q1

A's salary is 25% more than B's salary. By what percentage is B's salary less than A's salary?

  1. (1)20%
  2. (2)16⅔%
  3. (3)25%
  4. (4)80%

Answer: (1) 20%

Explanation

B is less by 25/125 × 100 = 20%.

Q2

A shopkeeper marks his goods 40% above the cost price and then allows a discount of 15% on the marked price. What is his profit percentage?

  1. (1)25%
  2. (2)19%
  3. (3)21%
  4. (4)17.5%

Answer: (2) 19%

Explanation

SP = 140 × 0.85 = 119 for CP 100, so profit = 19%.

Q3

An article bought for ₹800 is sold for ₹920. What is the profit percentage?

  1. (1)12%
  2. (2)11.5%
  3. (3)13.04%
  4. (4)15%

Answer: (4) 15%

Explanation

Profit = ₹120; profit % = 120/800 × 100 = 15%.

Q4

A dishonest shopkeeper claims to sell at cost price but uses a weight of 900 g instead of 1 kg. What is his profit percentage?

  1. (1)12.5%
  2. (2)10%
  3. (3)9 1/11%
  4. (4)11 1/9%

Answer: (4) 11 1/9%

Explanation

He gains 100 g on every 900 g sold: 100/900 × 100 = 11 1/9%.

Q5

What is the third proportional to 4 and 6?

  1. (1)9
  2. (2)8
  3. (3)24
  4. (4)10

Answer: (1) 9

Explanation

If 4 : 6 = 6 : x, then x = 6²/4 = 9.

Q6

A starts a business with ₹40,000. After 5 months, B joins with ₹60,000. At the end of the year the total profit is ₹30,000. What is B's share?

  1. (1)₹16,000
  2. (2)₹14,000
  3. (3)₹12,000
  4. (4)₹18,000

Answer: (2) ₹14,000

Explanation

Ratio = 40,000 × 12 : 60,000 × 7 = 8 : 7; B's share = 30,000 × 7/15 = ₹14,000.

Q7

At simple interest, a sum of money becomes 3 times itself in 10 years. What is the rate of interest per annum?

  1. (1)11.6%
  2. (2)30%
  3. (3)20%
  4. (4)10%

Answer: (3) 20%

Explanation

Interest = 2P in 10 years, so rate = 200/10 = 20% per annum.

Q8

What is the difference between the compound interest (compounded annually) and the simple interest on ₹8,000 for 2 years at 5% per annum?

  1. (1)₹40
  2. (2)₹61
  3. (3)₹10
  4. (4)₹20

Answer: (4) ₹20

Explanation

Difference for 2 years = P(r/100)² = 8000 × (0.05)² = ₹20.

Q9

A sum of money at compound interest (compounded annually) amounts to ₹6,050 in 2 years and to ₹6,655 in 3 years. What is the sum?

  1. (1)₹5,000
  2. (2)₹4,840
  3. (3)₹5,445
  4. (4)₹5,500

Answer: (1) ₹5,000

Explanation

Rate = 605/6050 = 10%; sum = 6050/(1.1)² = ₹5,000.

Q10

A can finish a work in 12 days and B can finish it in 18 days. Working together, in how many days will they finish it?

  1. (1)30 days
  2. (2)7.2 days
  3. (3)15 days
  4. (4)6 days

Answer: (2) 7.2 days

Explanation

Together per day = 1/12 + 1/18 = 5/36, so time = 36/5 = 7.2 days.

Q11

A and B together can do a work in 10 days, B and C together in 15 days, and C and A together in 12 days. In how many days can A, B and C together do it?

  1. (1)4 days
  2. (2)12⅓ days
  3. (3)8 days
  4. (4)6⅙ days

Answer: (3) 8 days

Explanation

2(A + B + C) = 1/10 + 1/15 + 1/12 = 1/4, so A + B + C = 1/8 per day: 8 days.

Q12

Pipes A and B can fill a tank in 20 minutes and 30 minutes respectively, while pipe C can empty the full tank in 15 minutes. If all three are opened together on the empty tank, in how much time will it be filled?

  1. (1)35 minutes
  2. (2)6⅔ minutes
  3. (3)12 minutes
  4. (4)60 minutes

Answer: (4) 60 minutes

Explanation

Net filling per minute = 1/20 + 1/30 − 1/15 = 1/60, so the tank fills in 60 minutes.

Q13

A car goes from Jaipur to Ajmer at 60 km/h and returns along the same route at 40 km/h. What is its average speed for the whole journey?

  1. (1)48 km/h
  2. (2)52 km/h
  3. (3)50 km/h
  4. (4)24 km/h

Answer: (1) 48 km/h

Explanation

Average speed = 2xy/(x + y) = 2 × 60 × 40/100 = 48 km/h.

Q14

A train 240 m long running at 54 km/h crosses a platform 210 m long. How much time does it take?

  1. (1)16 seconds
  2. (2)30 seconds
  3. (3)14 seconds
  4. (4)8⅓ seconds

Answer: (2) 30 seconds

Explanation

54 km/h = 15 m/s; distance = 240 + 210 = 450 m; time = 450/15 = 30 seconds.

Q15

Two trains 150 m and 100 m long are running on parallel tracks in the same direction at 72 km/h and 54 km/h respectively. How long will the faster train take to completely pass the slower one?

  1. (1)40 seconds
  2. (2)13 8/9 seconds
  3. (3)50 seconds
  4. (4)7 1/7 seconds

Answer: (3) 50 seconds

Explanation

Relative speed = 72 − 54 = 18 km/h = 5 m/s; distance = 150 + 100 = 250 m; time = 250/5 = 50 seconds.

Q16

A boat covers 30 km downstream in 2 hours and 18 km upstream in 3 hours. What is the speed of the stream?

  1. (1)6 km/h
  2. (2)10.5 km/h
  3. (3)9 km/h
  4. (4)4.5 km/h

Answer: (4) 4.5 km/h

Explanation

Downstream = 15 km/h, upstream = 6 km/h; stream speed = (15 − 6)/2 = 4.5 km/h.

Q17

The sum of the present ages of a father and his son is 60 years. Six years ago, the father's age was five times the son's age. What is the son's present age?

  1. (1)14 years
  2. (2)10 years
  3. (3)46 years
  4. (4)8 years

Answer: (1) 14 years

Explanation

F + S = 60 and F − 6 = 5(S − 6) give 6S − 24 = 60, so S = 14 years.

Q18

In what ratio must rice costing ₹40 per kg be mixed with rice costing ₹55 per kg so that the mixture is worth ₹45 per kg?

  1. (1)8 : 11
  2. (2)2 : 1
  3. (3)9 : 8
  4. (4)1 : 2

Answer: (2) 2 : 1

Explanation

By alligation, cheaper : dearer = (55 − 45) : (45 − 40) = 10 : 5 = 2 : 1.

Q19

A container has 40 litres of pure milk. 4 litres of milk is taken out and replaced with water. This process is done 3 times in all. How much milk is now left in the container?

  1. (1)26.24 litres
  2. (2)28 litres
  3. (3)29.16 litres
  4. (4)32.4 litres

Answer: (3) 29.16 litres

Explanation

Milk left = 40 × (1 − 4/40)³ = 40 × 0.729 = 29.16 litres.

Q20

Consider the following statements: 1. 30% of 70 is equal to 70% of 30. 2. If a town's population increases by 10% in one year and decreases by 10% in the next, it returns to its original value. 3. Two successive increases of 10% each are equal to a single increase of 21%. Which of the statements given above are correct?

  1. (1)1 and 2 only
  2. (2)2 and 3 only
  3. (3)1 and 3 only
  4. (4)1, 2 and 3

Answer: (3) 1 and 3 only

Explanation

Both 30% of 70 and 70% of 30 equal 21; 1.1 × 1.1 = 1.21 gives 21%. Statement 2 is wrong: 1.1 × 0.9 = 0.99, a net 1% fall.