IBPS Arithmetic Word Problems Questions and Answers — Questions and Answers
Question 1: The average age of 30 students in a class is 14 years. When the age of the class teacher is included, the average age of the class becomes 15 years. What is the age of the class teacher?
- 45 years (Correct answer)
- 44 years
- 42 years
- 46 years
Correct answer: 45 years
The initial total age of the 30 students is 30 * 14 = 420 years. When the teacher is included, the total number of people becomes 31, and the new average age is 15 years. The new total age is 31 * 15 = 465 years. The age of the teacher is the difference between the new total age and the initial total age: 465 - 420 = 45 years.
Question 2: A container holds a mixture of milk and water in the ratio 7:3. When 20 litres of the mixture are drawn off and replaced with 20 litres of water, the ratio of milk to water becomes 1:1. What was the initial quantity of the mixture in the container?
- 80 litres
- 70 litres (Correct answer)
- 60 litres
- 90 litres
Correct answer: 70 litres
Let the initial quantities of milk and water be 7x and 3x litres. Total mixture = 10x. When 20 litres are removed, the milk removed is (7/10)*20 = 14 litres and water removed is (3/10)*20 = 6 litres. The remaining quantities are (7x-14) of milk and (3x-6) of water. After adding 20 litres of water, the new quantity of water is (3x-6)+20 = 3x+14. The new ratio is (7x-14) / (3x+14) = 1/1. Solving this gives 7x-14 = 3x+14, which simplifies to 4x = 28, so x=7. The initial quantity of the mixture was 10x = 10*7 = 70 litres.
Question 3: A shopkeeper marks an article 60% above its cost price. He then sells it after allowing a discount of 25% on the marked price. If his profit in the transaction is ₹440, what is the cost price of the article?
- ₹2000
- ₹2400
- ₹2200 (Correct answer)
- ₹2500
Correct answer: ₹2200
Let the Cost Price (CP) be 'x'. The Marked Price (MP) is x + 60% of x = 1.6x. The discount is 25% of MP, so the Selling Price (SP) is 75% of MP. SP = 0.75 * 1.6x = 1.2x. Profit is SP - CP = 1.2x - x = 0.2x. Given that the profit is ₹440, we have 0.2x = 440. Therefore, x = 440 / 0.2 = ₹2200.
Question 4: The difference between the compound interest and simple interest on a certain sum of money for 2 years at a rate of 15% per annum is ₹900. What is the principal amount?
- ₹36,000
- ₹42,000
- ₹45,000
- ₹40,000 (Correct answer)
Correct answer: ₹40,000
The formula for the difference between compound interest (CI) and simple interest (SI) for 2 years is: Difference = P * (R/100)^2, where P is the principal and R is the rate of interest. Plugging in the values: 900 = P * (15/100)^2. This simplifies to 900 = P * (3/20)^2, which is 900 = P * (9/400). Solving for P gives P = (900 * 400) / 9 = 100 * 400 = ₹40,000.
Question 5: A can complete a piece of work in 24 days and B can complete the same work in 36 days. They start working together, but A leaves 8 days before the completion of the work. For how many days did the work last?
- 15.6 days
- 18.4 days
- 19.2 days (Correct answer)
- 20.8 days
Correct answer: 19.2 days
Let the total time be 'x' days. B works for all 'x' days, while A works for (x-8) days. A's one-day work is 1/24 and B's is 1/36. The total work done is 1. So, the equation is (x-8)/24 + x/36 = 1. The LCM of 24 and 36 is 72. Multiplying the equation by 72 gives 3(x-8) + 2x = 72. This simplifies to 3x - 24 + 2x = 72, or 5x = 96. Therefore, x = 96/5 = 19.2 days.
Question 6: A train running at a speed of 72 km/hr crosses a man standing on a platform in 12 seconds and crosses the platform completely in 30 seconds. What is the length of the platform?
- 240 metres
- 300 metres
- 360 metres (Correct answer)
- 400 metres
Correct answer: 360 metres
First, convert the speed to m/s: 72 km/hr * (5/18) = 20 m/s. When the train crosses a man, the distance covered is its own length. Length of Train = Speed * Time = 20 m/s * 12 s = 240 metres. When the train crosses a platform, the distance covered is the length of the train plus the length of the platform. (Length of Train + Length of Platform) = Speed * Time = 20 m/s * 30 s = 600 metres. So, Length of Platform = 600 m - 240 m = 360 metres.
IBPS Arithmetic Word Problems Questions and Answers
The average age of 30 students in a class is 14 years.
When the age of the class teacher is included, the average age of the class becomes 15 years.
What is the age of the class teacher?