๐ Age-Based Problems
Q1. The sum of the ages of a father and his son is 45 years. Five years ago, the father's age was four times the age of the son. Find their present ages.
Q2. The present age of a woman is 3 times the present age of her daughter. After 12 years, she will be twice as old as her daughter. Find their present ages.
Q3. Seven years ago, Asha was five times as old as Nisha. Seven years hence, she will be twice as old. Find their present ages.
๐ Speed, Distance & Time
Q4. A train travels 360 km at uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less. Find the speed of the train and time taken.
Q5. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it goes 40 km upstream and 55 km downstream. Find the speed of the boat in still water and the speed of the stream.
Q6. Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
๐ Geometry-Based Problems
Q7. The perimeter of a rectangle is 44 cm. If the length is increased by 4 cm and the breadth is decreased by 2 cm, the area remains the same. Find the dimensions of the rectangle.
Q8. The angles of a triangle are x, y, and 45ยฐ. If the difference of the two unknown angles is 15ยฐ, find the value of x and y.
Q9. In a rectangle, if the length is reduced by 5 cm and the breadth is increased by 3 cm, it becomes a square. Also, the perimeter of this square is 4 cm less than the perimeter of the rectangle. Find its dimensions.
๐ฐ Money & Coins
Q10. A bag contains โน5 and โน10 coins. If the total number of coins is 30 and the total amount is โน200, find the number of coins of each type.
Q11. The cost of 5 oranges and 3 apples is โน35 and the cost of 2 oranges and 4 apples is โน28. Find the cost of each.
๐งช Mixture Problems
Q12. A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution. 640 litres of the 8% solution are required to be diluted. If a pharmacist needs 80 litres of the final 6% solution, how many litres of each should be mixed?
Q13. One says, "Give me hundred, friend! I shall then become twice as rich as you." The other replies, "If you give me ten, I shall be six times as rich as you." Find the amount each person has.
โญ Miscellaneous / Real-Life
Q14. In a class test, the sum of marks obtained by Ravi in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 less in Science, the product of marks would have been 180. Find the marks in each subject.
Q15. The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is increased by 27. Find the number.