The cost of papering four walls of a room at 70 paisa per square metre is Rs. 157.50. The height of the room is 5 metres. Find the length and the breadth of the room if they are in the ratio 4 : 1.
Question
The cost of papering four walls of a room at 70 paisa per square metre is Rs. 157.50. The height of the room is 5 metres. Find the length and the breadth of the room if they are in the ratio 4 : 1.
Solution
Sure, let's solve this step by step.
Step 1: Convert the cost to paisa. Rs. 157.50 = 15750 paisa.
Step 2: Calculate the total area of the walls. Since the cost of papering is 70 paisa per square metre, the total area would be 15750/70 = 225 square metres.
Step 3: The total area of the four walls of the room is 2*(length + breadth)height. Given that the height is 5 metres, the sum of the length and the breadth would be 225/25 = 22.5 metres.
Step 4: It's given that the length and the breadth are in the ratio 4:1. So, we can divide 22.5 in the ratio 4:1 to get the length and the breadth.
Length = 4/5 * 22.5 = 18 metres. Breadth = 1/5 * 22.5 = 4.5 metres.
So, the length and the breadth of the room are 18 metres and 4.5 metres respectively.
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