Arithmetic Questions

Arithmetic Questions have been provided to help you improve your numerical skills. Arithmetic involves basic operations of addition, subtraction, multiplication, and division. Mastering these calculations in maths is essential for everyone. The step-by-step solutions to the arithmetic problems given here will help you brush up on your arithmetic abilities and be more confident in handling numbers.

Arithmetic Questions with Solutions

Question 1: If a pen costs $2.50 and a notebook costs $3.75, how much will 4 pens and 3 notebooks cost?

Solution:

Find the cost of 4 pens.
Each pen costs $2.50.
4 pens cost 4 × $2.50 = $10.00.

Find the cost of 3 notebooks.
Each notebook costs $3.75.
3 notebooks cost 3 × $3.75 = $11.25.

Calculate the total cost.
Total cost = Cost of pens + Cost of notebooks
Total cost = $10.00 + $11.25 = $21.25.

Question 2: A fruit seller has 123 apples. If he sells 47 apples, how many apples will he have left?

Solution:

Start with the initial number of apples.
Initial apples = 123.

Subtract the number of apples sold.
Apples sold = 47.
Remaining apples = 123 – 47.

Calculate the final number of apples.
Remaining apples = 76.

Question 3: A chocolate box has 15 chocolates, and a party pack contains 3 such boxes. How many chocolates are there in 5 party packs?

Solution:

Calculate chocolates in one party pack.
One box has 15 chocolates.
One party pack (3 boxes) has 3 × 15 = 45 chocolates.

Find chocolates in 5 party packs.
5 party packs have 5 × 45 chocolates.
Total chocolates = 225.

Question 4: A baker baked 250 cookies. He sold 175 of them and then made 75 more. How many cookies does he have now?

Solution:

Start with initial cookies baked.
Initial cookies = 250.

Subtract the cookies sold.
Cookies sold = 175.
Cookies after selling = 250 – 175 = 75.

Add the new cookies made.
New cookies made = 75.
Total cookies now = 75 + 75 = 150.

Question 5: A school ordered 45 books for its library. If each book costs $12, what is the total cost for all the books?

Solution:

Calculate the cost of one book.
One book costs $12.
Multiply the cost of one book by the total number of books.
Total books = 45.
Total cost = 45 × $12.
Total cost = $540.

Question 6: A car travels 150 kilometers in 3 hours. How many kilometers will it travel in 7 hours at the same speed?

Solution:

Find the distance traveled in one hour.
Distance in 3 hours = 150 km.
Distance in 1 hour = 150 km ÷ 3.
Distance in 1 hour = 50 km.
Calculate the distance for 7 hours.
Distance in 7 hours = 50 km/hour × 7.
Distance in 7 hours = 350 km.

Question 7: There are 60 students in a class, and 3/5 of them are girls. How many boys are in the class?

Solution:

Calculate the number of girls.
Fraction of girls = 3/5.
Number of girls = 3/5 × 60.
Number of girls = 36.
Find the number of boys.
Total students = 60.
Number of boys = Total students – Number of girls.
Number of boys = 60 – 36.
Number of boys = 24.

Question 8: A rectangle has a length of 20 cm and a width of 15 cm. What is its area?

Solution:

Calculate the area of the rectangle.
Area = Length × Width.
Area = 20 cm × 15 cm.
Area = 300 cm².

Question 9: A train travels 320 km in 4 hours. At the same speed, how long will it take to travel 480 km?

Solution:

Find the speed of the train.
Speed = Distance ÷ Time.
Speed = 320 km ÷ 4 hours.
Speed = 80 km/hour.
Calculate the time to travel 480 km.
Time = Distance ÷ Speed.
Time = 480 km ÷ 80 km/hour.
Time = 6 hours.

Question 10: If you buy 3 notebooks and each costs $5, and you pay with a $20 bill, how much change will you receive?

Solution:

Calculate the total cost of the notebooks.
Cost of one notebook = $5.
Total cost = 3 × $5.
Total cost = $15.
Find the change received.
Change = Amount paid – Total cost.
Change = $20 – $15.
Change = $5.

Related Links:

• Basic Arithmetic Operations
• Addition
• Subtraction
• Multiplication
• Division

Question 11: A rectangle’s length is twice its width. If the width is 8 cm, what is the perimeter of the rectangle?

Solution:

Calculate the length of the rectangle.
Length = 2 × Width.
Length = 2 × 8 cm.
Length = 16 cm.
Find the perimeter.
Perimeter = 2 × (Length + Width).
Perimeter = 2 × (16 cm + 8 cm).
Perimeter = 2 × 24 cm.
Perimeter = 48 cm.

Question 12: A bottle contains 1.5 liters of water. If you pour out 500 ml, how much water is left in the bottle?

Solution:

Convert the initial volume to milliliters.
Initial volume = 1.5 liters = 1500 ml.
Subtract the volume of water poured out.
Water poured out = 500 ml.
Remaining water = 1500 ml – 500 ml.
Remaining water = 1000 ml.

Question 13: A school has 8 classes with 35 students in each class. How many students are there in total?

Solution:

Calculate the total number of students.
Number of students in one class = 35.
Total students = Number of classes × Number of students in one class.
Total students = 8 × 35.
Total students = 280.

Question 14: A rectangle has a length that is 4 times its width. If the perimeter of the rectangle is 100 cm, what are its length and width?

Solution:

Let the width of the rectangle be x cm.
Then, the length is 4x cm.
The perimeter of a rectangle is 2 times the sum of its length and width.
So, 100 cm = 2 × (4x + x).
Simplifying, 100 cm = 10x.
Solving for x, x = 10 cm.
Therefore, the width is 10 cm, and the length is 40 cm (4 times the width).

Question 15: A train covers a distance of 360 km at a certain speed. If the speed is increased by 20 km/h, it takes one hour less to cover the same distance. What was the original speed of the train?

Solution:

Let the original speed of the train be v km/h.
Time taken at original speed = 360/v hours.
New speed = v + 20 km/h.
Time taken at new speed = 360/(v + 20) hours.
According to the problem, 360/v – 360/(v + 20) = 1.
Multiplying through by v(v + 20) gives 360(v + 20) – 360v = v² + 20v.
This simplifies to 7200 = v² + 20v.
Rearranging gives v² + 20v – 7200 = 0.
Solving this quadratic equation will give the original speed v.

Question 16: A rectangular garden is 20 meters longer than it is wide. If the area of the garden is 300 square meters, what are its dimensions?

Solution:

Let the width of the garden be w meters.
Then the length is w + 20 meters.
Area of the garden = length × width = w(w + 20).
Setting the area to 300 gives w(w + 20) = 300.
This simplifies to w² + 20w – 300 = 0.
Solving this quadratic equation gives the width w.
The length can be found by adding 20 to the width.

Question 17: Water is being pumped into a tank at a rate of 40 liters per minute. If the tank already contains 120 liters of water, how long will it take for the tank to hold 320 liters?

Solution:

First, calculate the additional amount of water needed to fill the tank to 320 liters.
Required additional water = 320 liters – 120 liters = 200 liters.
Pumping rate = 40 liters/minute.
Time to fill = Required additional water ÷ Pumping rate.
Time to fill = 200 liters ÷ 40 liters/minute = 5 minutes.
Thus, it will take 5 minutes to fill the tank to 320 liters.

Question 18: If 3 times a number increased by 10 is equal to 28, what is the number?

Solution:

Let the number be x.
According to the problem, 3x + 10 = 28.
Subtracting 10 from both sides, 3x = 18.
Dividing both sides by 3, x = 18 ÷ 3 = 6.
Therefore, the number is 6.

Question 19: A bookshelf has 3 shelves with an equal number of books. If 5 books are added to each shelf, the total number of books becomes 75. How many books were on each shelf initially?

Solution:

Let the initial number of books on each shelf be x.
After adding 5 books to each shelf, the number of books per shelf is x + 5.
With 3 shelves, the total number of books becomes 3(x + 5).
Setting this equal to 75, we have 3(x + 5) = 75.
Solving for x, 3x + 15 = 75.
Subtracting 15 from both sides, 3x = 60.
Dividing by 3, x = 60 ÷ 3 = 20.
Thus, initially, there were 20 books on each shelf.

Question 20: A quadratic equation is represented as ax² + bx + c = 0. If the equation 2x² – 4x – 6 = 0 has roots α and β, find the value of α² + β².

Solution:

The sum of the roots α + β is given by -b/a, and the product of the roots αβ is c/a.
For the equation 2x² – 4x – 6 = 0:
a = 2, b = -4, and c = -6.
Sum of roots α + β = -(-4)/2 = 2.
Product of roots αβ = -6/2 = -3.
The value of α² + β² is (α + β)² – 2αβ.
Substituting the known values, α² + β² = 2² – 2(-3) = 4 + 6 = 10.

Question 21: A person invests $1000 in a savings account with an annual interest rate of 5% compounded annually. How much will be in the account after 10 years?

Solution:

The final amount in a compound interest account is given by the formula P(1 + r/n)^nt,
where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case:
– Principal (P) = $1000
– Annual interest rate (r) = 5% = 0.05
– Compounded annually, so n = 1
– Time period (t) = 10 years
Substituting these values into the formula, the final amount is calculated as follows:
Final amount = 1000(1 + 0.05/1)^1×10 = 1000(1.05)¹⁰.
Calculating this, the final amount ≈ $1628.89.

Question 22: The sum of the squares of two consecutive even numbers is 340. Find the numbers.

Solution:

Let the first even number be x.
The next consecutive even number is x + 2.
The equation becomes x² + (x + 2)² = 340.
Expanding the equation: x² + x² + 4x + 4 = 340.
Combining like terms: 2x² + 4x – 336 = 0.
Solving this quadratic equation will give the values of x, which are the required numbers.

Question 23: If 10 is subtracted from four times a number, the result is equal to adding 20 to twice the number. Find the number.

Solution:

Let the number be y.
According to the problem, 4y – 10 = 2y + 20.
Bringing like terms to one side: 4y – 2y = 20 + 10.
Simplifying: 2y = 30.
Dividing both sides by 2: y = 15.
Therefore, the number is 15.

Question 24: A ladder is leaning against a wall. The top of the ladder is 15 ft from the ground and forms a 60-degree angle with the wall. Find the length of the ladder.

Solution:

Using trigonometry, cos(60°) = adjacent/hypotenuse.
Here, adjacent = height of the wall = 15 ft, and hypotenuse = length of the ladder.
cos(60°) = 0.5 (cosine value of 60 degrees).
So, 0.5 = 15/length of the ladder.
Multiplying both sides by the length of the ladder and then by 2: length of the ladder = 30 ft.
Therefore, the length of the ladder is 30 ft.

Question 25: The difference between the compound interest and simple interest on a certain amount of money at 10% per annum for 2 years is $50. Find the principal.

Solution:

Let the principal amount be P.
Simple Interest (SI) = P × rate × time = P × 10% × 2.
Compound Interest (CI) is calculated using the formula P(1 + r/n)^nt – P.
Here, r = 10%, n = 1, t = 2.
CI = P(1 + 10%/1)^1×2 – P = P(1.1)² – P.
Difference between CI and SI = CI – SI = $50.
Substituting the formulas for CI and SI and solving for P will give the principal amount.

Conclusion

The Solutions to these Arithmetic Questions would provide you with the necessary tools to be better with numbers in general. By practising these problems, you will gain a very good understanding of how to approach and simplify numerical expressions.