Question
The length of a rectangle is 2 cm more than the radius
of a circle. The perimeter of the rectangle is 108 cm, and the ratio of its length to breadth is 5:4. Find the difference between the area of the circle and the area of the rectangle.Solution
ATQ, Let the length and breadth of the rectangle be 5a cm and 4a cm, respectively. Perimeter of the rectangle = 2 × (Length + Breadth) 108 = 2 × (5a + 4a) 108 = 2 × 9a 108 = 18a a = 6 Length of the rectangle = 5a = 5 × 6 = 30 cm Breadth of the rectangle = 4a = 4 × 6 = 24 cm The radius of the circle = 30 − 2 = 28 cm Area of the circle = πr² = 22/7 × 28 × 28 = 2464 cm² Area of the rectangle = 30 × 24 = 720 cm² Required difference = 2464 − 720 = 1744 cm²
Akshay invested Rs. 1950 in two schemes P and Q in the respective ratio of 8:5. Scheme P and Q are offering simple interest at the rate of 8% per annum ...
Rs.5,000 is divided into two parts such that if one part is invested at 4% and the other at 5%, then the whole annual interest from both sums is Rs.223....
Krishna invests a certain amount at an annual simple interest rate of 9% for 2 years. The total amount he receives after this period is then reinvested ...
A sum is lent on compound interest for 2 years at 13% p.a. If the compound interest on the sum is Rs.3045.9, find the sum.
- Divya invested Rs. 'd' in scheme A and Rs. (d + 850) in scheme B for 2 years each. Scheme A offers 13% simple interest per annum, while scheme B offers 9% ...
Pawan invested Rs. 12,000 in a Systematic Investment Plan (SIP) that provides compound interest at an annual rate of 25%, compounded yearly for 2 years....
Anjali invested Rs.15000 in a scheme offering compound interest of x% p.a. compounded annually. If at the end of 2 years, interest received by her from ...
A sum when invested at simple interest of 10% p.a. becomes Rs. 1,680 in 4 years. If the same sum was invested at compound interest of 20% p.a. for 2 yea...
An equal sum of money is invested in two schemes which offer interest at the same rate but one at simple interest and the other at compound interest (co...
A man invested Rs. 10,000 at simple interest of 15% p.a. If he had instead invested the same sum on compound interest of 15% p.a., compounded annually, ...
Relevant for Exams:
