Medium
Mathematical Puzzles
Challenging mathematical puzzles involving numbers, patterns and calculations.
Mathematical Puzzles Puzzles
Hard
A number is 30% less than 200. What is the number?
Hard
The product of two consecutive positive integers is 156. What are the integers?
Expert
A three-digit number has digits whose sum is 12. The hundreds digit is twice the tens digit, and the units digit is three more than the tens digit. What is the number?
Hard
A tank contains 90 litres of water. One-third of the water is removed and replaced with an equal amount of clean water. How much of the original water remains?
Medium
The average of five numbers is 24. Four of the numbers are 18, 22, 25 and 30. What is the fifth number?
Hard
A number is increased by 20% and becomes 180. What was the original number?
Hard
A two-digit number has digits whose sum is 11. Reversing the digits increases the number by 27. What is the original number?
Hard
A father is three times as old as his son. In 12 years, the father will be twice as old as his son. How old are they now?
Medium
A number is multiplied by 5 and then reduced by 12. The result is 38. What is the number?
Hard
A shopkeeper buys an item for ₹500 and sells it for ₹575. What is the profit percentage?
Hard
A can contains 60 litres of a mixture of milk and water in the ratio 2:1. How much water must be added to make the ratio 1:1?
Expert
A positive integer is divisible by both 12 and 18. What is the smallest possible integer greater than 100?
Hard
A rectangular garden is 20 m long and 14 m wide. A path 1 m wide is built inside along all four sides. What is the area of the remaining garden?
Expert
A sequence is defined by a₁ = 3 and aₙ = aₙ₋₁ + 4. What is a₁₀?
Medium
A number is increased by 15 and then multiplied by 2. The result is 50. What was the original number?
Medium
The sum of three consecutive odd numbers is 99. What is the largest number?
Hard
A number is divided by 4, then 7 is added. The result is 19. What is the number?
Medium
A shop gives a 25% discount on an item marked at ₹800. What is the selling price?
Hard
A train travels 180 km in 2 hours 15 minutes. What is its average speed in km/h?
Hard
A rectangle has an area of 96 cm² and a width of 8 cm. What is its perimeter?
Hard
The ratio of boys to girls in a class is 3:2. If there are 35 students, how many are girls?
Expert
A positive integer leaves remainder 2 when divided by 5 and remainder 3 when divided by 7. What is the smallest such integer?
Expert
A square has the same perimeter as a rectangle measuring 14 cm by 6 cm. What is the area of the square?
Hard
A three-digit number has digits that add up to 15. The hundreds digit is twice the units digit, and the tens digit is 3 more than the units digit. What is the number?
Medium
Five consecutive integers have a sum of 85. What are the five integers?
Medium
A two-digit number has digits whose sum is 10 and whose product is 24. The tens digit is smaller than the units digit. What is the number?
Medium
Three consecutive even numbers have a sum of 78. Find the numbers.
Medium
A father is three times as old as his son. Eight years from now, the father will be twice as old as the son. How old are they now?
Medium
A rectangle has a perimeter of 50 cm. Its length is 3 cm greater than its width. Find its dimensions.
Medium
The average of five numbers is 24. Four of the numbers are 18, 22, 25 and 31. What is the fifth number?
Hard
A price is increased by 20% and then decreased by 20%. What is the overall percentage change?
Hard
A can complete a job in 12 days and B can complete it in 18 days. If they work together at constant rates, how long will they take?
Hard
A tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours. If both pipes are opened together, how long will the empty tank take to fill?
Hard
A two-digit number has digits whose sum is 11. When the digits are reversed, the new number is 27 greater than the original number. What is the original number?
Expert