In the center of square room with sides 10 m, there is a square of turkey carpet and the rest of the floor is covered with oil cloth. The carpet and the oil cloth cost Rs. 15 Rs. 6.50 respectively per square meter and the total cost of the carpet and the oil cloth is 1,338.50. What is the width of the Oil cloth border?
In the center of square room with sides 10 m, there is a square of turkey carpet and the rest of the floor is covered with oil cloth. The carpet and the oil cloth cost Rs. 15 Rs. 6.50 respectively per square meter and the total cost of the carpet and the oil cloth is 1,338.50. What is the width of the Oil cloth border? Correct Answer ½ meter
Given
Side of room = 10 m
The carpet and the oil cloth cost Rs. 15 Rs. 6.50 respectively per square meter and the total cost of the carpet and the oil cloth is 1,338.50.
Formula
Area of square = a2, where a = side of the square
Calculation
Let the side of turkey carpet be a.
Hence, area of turkey carpet = a2
Total area of room = 102 = 100 m2
Hence, area of oil cloth = 100 - a2
Cost of turkey carpet = 15 × a2
Cost of oil cloth = (100 - a2) × 6.5
Total cost = 15 × a2 + (100 - a2) × 6.5
⇒ 15a2 + 650 - 6.5a2 = 1,338.50
⇒ 8.5a2 = 688.5
⇒ a2 = 81
⇒ a = 9
Hence, width of oil cloth = (10 - 9)/2 = 1/2 m
(Note : Here, we have to divide (10 - 9) by 2 as extra width of oil cloth is on the both sides of turkey carpet)
