Question : The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m2. What is the width of this rectangle?
Option 1: 12 m
Option 2: 10 m
Option 3: 8 m
Option 4: 15 m
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 8 m
Solution : Given, The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m 2 . We know, Area of rectangle = length × width Let the width of the rectangle be $x$. ⇒ The length is $\frac{3x}{2}$ and the area of the rectangle is $\frac{3x^2}{2}$ Now, the length is increased by 25%, So, the new length is $\frac{3x}{2}×(1+\frac{25}{100})=\frac{3x}{2}\times(1.25)=\frac{15x}{8}$ And the area is $\frac{15x^2}{8}$ According to the question, $\frac{15x^2}{8}=\frac{3x^2}{2}+24$ ⇒ $(\frac{15−12}{8})x^2=24$ ⇒ $x^2=\frac{24×8}{3}$ ⇒ $x^2=64$ ⇒ $x=\sqrt{64}$ ⇒ $x=8$ m Hence, the correct answer is 8 m.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : The difference between the length and breadth of a rectangle is 40 metres. If its perimeter is 96 metres, then what will be the area of the rectangle?
Question : The length and the breadth of a rectangle are increased by 15% and 10%, respectively. What is the percentage increase in the area of the rectangle?
Question : If a storeroom of a house is in the shape of a cuboid having a length of 3 m, a width of 2 m, and a height of 4 m, find the total area of its four walls.
Question : The length of each diagonal of a rectangle is 50 cm. If its breadth is 14 cm, then what will be the area of the rectangle?
Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile