Question

There is a square field whose side is 44m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and graving the path at Rs 2. 75 and Rs. 1.5 per square metre, respectively, is Rs 4,904. Find the width of the gravel path. 

Answer 1

Let the side of flower bed be a and that of gravel path be b. 

Then a + 2b = 44 (as 44 is overall size of field and it contains side of flower bed and double side of gravel path) .... (i) 

Area of Flower bed = a² 

Area of Gravel path = Area of Square - Area of flower bed = 44 x 44 - a² 

⇒ Area of Gravel path = 1936 - a²

Cost of laying flower bed + Gravel path = Area x cost of laying per sq.m 

⇒  4904 = (a² x 2.75) + (1936 - a²) x 1.5 

⇒ 4904 = 2.75a² -1.5 a² + 2904 

⇒ 1.25 a² = 2000 

⇒ a² = 1600, Hence a = 40. 

Hence gravel path width =  ${\displaystyle \frac{44-40}{2}}$ m = 2 m