Question
Tom can paint one side of a triangular wall of base 16
metres and height 21 metres in 14 days. Ram can paint 75% of one side of a rectangular wall of length ___ metres and breadth 24 metres in 21.6 days. There is a circular wall of diameter 42 metres. If Tom and Ram work together for 30 days on painting the circular wall, then they would have finished painting one side and painted 324 m² of the other side.  (Note: Thickness of all the walls are negligible). What is the value that will come in place of the blank?Solution
Area of one side of the triangular wall = (1/2) × base × height = (1/2) × 16 × 21 = 168 m²
So, painting efficiency of Tom = 168 ÷ 14 = 12 m²/day
Area of one side of the circular wall = π × r² = (22/7) × (42/2) × (42/2) = (22/7) × 21 × 21 = 1386 m²
So, total area painted by Ram and Tom = 1386 + 324 = 1710 m²
Out of which, area painted by Tom = 30 × 12 = 360 m²
So, area painted by Ram = 1710 - 360 = 1350 m²
So, painting efficiency of Ram = 1350 ÷ 30 = 45 m²/day
So, area painted by Ram in 21.6 days = 45 × 21.6 = 972 m² = 75% of the area of one side of the rectangular wall
So, 100% of area of one side of the rectangular wall = 972 ÷ 0.75 = 1296 m²
And so, length of the rectangular wall = 1296 ÷ 24 = 54 meters
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