Mathematics
Word Problems and Applications
Practice questions
A square park has area (196). If its side is increased by (4), what will be the new area?The square of a number is 54 more than 15 times the number. What is the positive number?The sum of two numbers is (26) and the sum of their squares is (340). What is the larger number?The product of two positive numbers is 378, and the larger number is 3 more than the smaller number. Find the smaller number.The area of a rectangular room is 432 square units, and its length is 6 units more than its breadth. What is the breadth of the room?The breadth of a rectangle is 9 units. Its length is four times the number obtained by subtracting 3 units from the breadth. What is the area of the rectangle?For which positive number does multiplying the number by the result obtained after adding 8 to it give 209?When 6 is subtracted from a number and the result is multiplied by the same number, the product is 135. What is the positive number?A poster has an area of \(216\) square units. Its length is \(6\) units more than its breadth. What is the breadth of the poster?A rectangular photo frame has outer length (24) and breadth (18). After removing a uniform border, the inner area is (280). What is the border width?A garden is 36 metres long and 24 metres wide. A uniform path runs inside along all four sides. The area of the portion left after making the path is 540 square metres. What is the width of the path?A rectangular field is 30 metres long and 18 metres wide. A path of uniform width is constructed all around the outside of the field. The total area of the field and the path is 748 square metres. What is the width of the path?A shopkeeper sells each item for \(x\) rupees and sells a total of \(80-x\) items. If his total revenue is 1500 rupees, what is the smaller value of \(x\)?In an examination, if the number of correct answers is \(x\), the marks obtained are \(x(30-x)\). If a student obtains 216 marks, what is the larger value of \(x\)?In a group, each person shakes hands with every other person exactly once. If the total number of handshakes is 66, how many people are in the group?In a tournament, each team plays exactly one match against every other team. If a total of 28 matches were played, how many teams participated?A rectangular plot has a perimeter of 60 metres and an area of 216 square metres. What is the length of its longer side?In a two-digit number, the tens digit is (3) more than the units digit and the product of the digits is (18). What is the number?In a work problem, person (A) takes (5) days less than person (B). Together they complete the work in (6) days. How many days will (B) alone take?The sum of squares of two consecutive positive integers is (841). What is the smaller integer?