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Q.

The cost of carpeting a room is Rs.120. if the width had been 4 meters less, the cost of the carpet would have been Rs.20 less. Then the width of the room is _______.


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a

24 m

b

20 m

c

18 m

d

18.5 m 

answer is A.

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Detailed Solution

We know that carpets are made in different forms and the cost of making a carpet is calculated on the area of the carpet. We also know that the area of the rectangle is the product of length (also called width) and breadth of the rectangle.
We are given the question that the cost of carpeting a room is Rs.120. Since we have to cover a rectangular room, the carpet will also be made in rectangular form. Let us assume the length of the rectangular carpet as l metre and the width of rectangular carpet as b metre. We can represent the cost rs.120 as the area in  m 2  . So we have;  l×b=120 ⇒b= 120 l ................(1)  
We are further given in the question that If the width had been 4 metres less, the cost of the carpet would have been Rs.20 less.
https://www.vedantu.com/question-sets/7a259e75-16e2-41f9-a2b5-14c55be7ec834743578634714150322.pngSo the new width is ( l  −4) m and the new area is 120 − 20 = 100 m 2  but the breadth is the same b. We have,
b( l  −4) = 100
We put the value of b from equation and put in above equation to have;
⇒ 120 l (l−4)=100  
We multiply both sides by bb to have;
⇒120 ( l  −4) = 100 l  
We divide both side of the equation by 20 to have;
⇒6( l  −4) = 5 l  
⇒6 l   − 24 = 5 l  
⇒6 − 5 l    = 24
So the width of the carpet is 24 m.
 
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