Mathematics
Word Problems and Applications
Practice questions
The denominator of a fraction is 4 more than its numerator. If 2 is added to both the numerator and denominator, the fraction becomes \(\frac{3}{5}\). What is the original numerator?The denominator of a fraction is (3) more than its numerator. If the sum of the fraction and its reciprocal is (\frac{29}{10}), what is the numerator?A train covers (360) km. If its speed were (5) km per hour more, it would take (1) hour less. What was the original speed?A bus travels (300) km. If its speed were (10) km per hour less, it would take (1) hour more. What is the actual speed?A boat goes (30) km downstream and (20) km upstream in (5) hours. The speed of the boat in still water is (12) km per hour. What is the speed of the current?A boat covers (24) km downstream and (16) km upstream in (4) hours. Its speed in still water is (10) km per hour. What is the speed of the current?A farmer has (100) m fencing to enclose three sides of a rectangular field along a wall. When will the maximum area occur?A rectangular park is to be fenced along two breadths and one length, with a total fencing of 96 m. What should its breadth be for the area of the park to be maximum?The difference between the length and breadth of a rectangle is 7 cm, and its area is 330 square cm. What is the perimeter of the rectangle?In a right triangle, the perpendicular is 7 cm longer than the base and the hypotenuse is 25 cm. What is the approximate length of the base?The two shorter sides of a right triangle are x cm and (x+2) cm, while its hypotenuse is 10 cm. What is the length of the larger of these two shorter sides?A ladder is (25) m long. When its foot is moved (7) m farther from the wall, its top comes (7) m down. What was the initial height on the wall?A ladder is (13) m long and its foot is (5) m from the wall. If the foot is moved (7) m farther away, by how many metres will the top come down?An object is thrown vertically upward. Its height t seconds after launch is \(h(t)=20t-5t^2\) metres. At what times will the object be at a height of 15 metres?The height of a ball is (h=30t-5t^2) m. When will it return to the ground?In a class, the total number of handshakes is (276). If each student shook hands once with every other student, how many students are there?In a tournament, each team plays exactly one match against every other team. If a total of 153 matches were played, how many teams participated in the tournament?In a book, the product of a page number and the number of the next page is 930. What is the smaller page number?A two-digit number has digit sum (11). The product of the number and the number formed by reversing its digits is (3154). What is the original number?A two-digit number has digit sum (12). The product of the number and its reversed number is (4032). Which can be the original number?