Mathematics
Word Problems and Applications
Practice questions
The length of a rectangle is (5,\text{cm}) more than its breadth and its area is (150,\text{cm}^2). What are the breadth and length?The product of two consecutive positive integers is 240. Which pair of integers is correct?A son's present age is \(x\) years, and his mother's present age is 20 years more than his. Five years ago, the product of their ages was 189. What is the son's present age?A car covers a distance of 240 km. If its speed is increased by 20 km/h, the travel time decreases by 1 hour. What was the car’s original speed?A uniform path is constructed all around inside a rectangular grassy plot that is 30 m long and 20 m wide. The area of the remaining grassy portion is 416 m². What is the width of the path?The product of two consecutive positive odd numbers is 255. Which numbers are they?One side of a right-angled triangle is 10 cm, and its hypotenuse is 5 cm longer than the other side. What is the length of the other side?In a two-digit number, the units digit is 1 more than the tens digit. The sum of the squares of the two digits is 61. What is the number?Worker A can complete a task alone in x days, while worker B can complete it alone in x+5 days. Together, they complete the task in 6 days. In how many days can worker A complete the task alone?The length of a rectangle is 4 metres more than its breadth, and its area is 96 square metres. What is the breadth of the rectangle?The sum of a positive number and its reciprocal is (\frac{5}{2}). What can the number be?The square of a positive number is 28 more than three times the number. What is the number?The area of a triangle is \(60\,\text{cm}^2\). Its base is \(4\,\text{cm}\) longer than its height. What is the height of the triangle?A ladder is placed against a wall. Its foot is \(x\) metres from the wall, and it reaches a height of \((x+7)\) metres on the wall. If the ladder is 13 metres long, what is the distance of its foot from the wall?A rectangular park has a perimeter of 50 m and an area of 150 m². What are its length and breadth?A total of 1200 rupees is spent on buying some items. If the price of each item decreases by 10 rupees, 4 more items can be bought for the same amount. What was the original price of each item?A boat takes 3 hours more to travel 48 km upstream than to travel the same distance downstream. The speed of the stream is 4 km/h. What is the speed of the boat in still water?The difference between two positive numbers is 6, and their product is 216. What is the smaller number?The sum of the squares of two consecutive natural numbers is 365. Which two numbers are they?The product of two consecutive positive even numbers is 224. Which numbers are they?