Mathematics
Word Problems and Applications
Practice questions
The diagonal of a rectangle is 25 cm, and its length is 5 cm greater than its breadth. What is the breadth of the rectangle?In a classroom, the number of rows is \(x\). Each row contains 3 more students than the number of rows. If there are 154 students in total, how many rows are there?A photograph has an outer length of 12 cm and breadth of 8 cm. A frame of uniform width is fitted around it, leaving an inner photograph area of 60 cm². What is the width of the frame?The sum of the square of a positive number and five times the number is 84. What is the number?A farmer uses 120 metres of fencing to enclose a rectangular field on all four sides. If the area of the field is 875 square metres, what are its length and breadth?The sum of two positive numbers is 19 and their product is 84. Which pair of numbers satisfies these conditions?The product of a positive number and the number 4 greater than it is 221. What is the smaller number?Two positive numbers differ by 9, and the sum of their squares is 585. What is the smaller number?A son's present age is \(x\) years, and his father is 28 years older than him. After 4 years, the product of their ages will be 960. What is the son's present age?Worker A alone completes a task in x days, while worker B alone completes it in (x+3) days. Together, they complete the same task in 2 days. In how many days will worker A alone complete the task?Two pipes fill a tank separately in \(x\) hours and \((x+4)\) hours, respectively. Working together, they fill the tank in \(\frac{24}{5}\) hours. How many hours will the faster pipe take to fill the tank alone?A vehicle covers a distance of 150 km. If its speed is increased by 5 km/h, the travel time decreases by 1 hour. What was its original speed?The length of a rectangle is 2 metres more than twice its breadth. If its area is \(180\ \text{m}^2\), what is its breadth?Some notebooks were bought for a total of 720 rupees. If the price of each notebook had been 6 rupees less, 4 more notebooks could have been bought for the same amount. What was the original price of each notebook?The hypotenuse of a right triangle is \(17\text{ cm}\), and one leg is \(7\text{ cm}\) longer than the other. What is the length of the shorter leg?The product of two consecutive positive multiples of 3 is 270. Which are these multiples?The two perpendicular sides of a right triangle are \(x\) cm and \((x+7)\) cm, and its hypotenuse is \((x+8)\) cm. What is the length of the smallest side?When the reciprocal of a positive number is subtracted from the number, the result is \(\frac{3}{2}\). What is the number?The sum of the ages of two people is 30 years and their product is 216. Find their ages.A bus covers a distance of 180 km. If its speed is reduced by 15 km/h, the travel time increases by 1 hour. What was its original speed?