This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the solutions to the problems: Question 9: If 5 men can build a house in 12 days, how many men are required to build the same house in 15 days? Step 1: Understand the inverse relationship. The number of men and the number of days are inversely proportional. This means that the total work (men × days) is constant. Let M_1 be the initial number of men and D_1 be the initial number of days. Let M_2 be the new number of men and D_2 be the new number of days. The formula is M_1 D_1 = M_2 D_2. Step 2: Substitute the given values. M_1 = 5 men, D_1 = 12 days. D_2 = 15 days. We need to find M_2. 5 men × 12 days = M_2 × 15 days Step 3: Solve for M_2. 60 = 15 M_2 M_2 = (60)/(15) M_2 = 4 men The number of men required is 4. --- Question 15: A cylindrical tin with base radius 28 cm and height 50 cm is filled with water. What is its capacity in litres? (Take 1000 cm^3 = 1 litre) Step 1: Calculate the volume of the cylinder in cubic centimeters. The formula for the volume of a cylinder is V = r^2 h. Given radius r = 28 cm and height h = 50 cm. We will use = (22)/(7). V = (22)/(7) × (28 cm)^2 × 50 cm V = (22)/(7) × 784 cm^2 × 50 cm V = 22 × 112 cm^2 × 50 cm V = 22 × 5600 cm^3 V = 123200 cm^3 Step 2: Convert the volume from cubic centimeters to litres. Given that 1000 cm^3 = 1 litre. Capacity in litres = 123200 cm^31000 cm^3/litre Capacity in litres = 123.2 litres The correct option is B. 123.2 litres. --- Question 16: An open rectangular tank has length 10 m, width 5 m and height 3 m. Find its surface area. Step 1: Identify the surfaces to be included in an open rectangular tank. An open tank has a bottom and four sides, but no top. The dimensions are: length (l) = 10 m, width (w) = 5 m, height (h) = 3 m. Step 2: Calculate the area of each surface. Area of the bottom = l × w = 10 m × 5 m = 50 m^2. Area of the two side faces = 2 × (l × h) = 2 × (10 m × 3 m) = 2 × 30 m^2 = 60 m^2. Area of the two front/back faces = 2 × (w × h) = 2 × (5 m × 3 m) = 2 × 15 m^2 = 30 m^2. Step 3: Sum the areas to find the total surface area. Total Surface Area = 50 m^2 + 60 m^2 + 30 m^2 Total Surface Area = 140 m^2 The correct option is A. 140 m^2. --- Question 17: Which of the figures below represents a cube? Step 1: Understand the definition of a cube. A cube is a three-dimensional solid object bounded by six square faces, with three meeting at each vertex. All edges are of equal length. Step 2: Examine each figure. • Figure A is a circle. • Figure B is a cylinder. • Figure C is a triangular prism. • Figure D is a cube. The correct option is D. --- Question 18: What is the supplement of 69^? Step 1: Understand supplementary angles. Two angles are supplementary if their sum is 180^. Step 2: Calculate the supplement. Let the supplementary angle be x. x + 69^ = 180^ x = 180^ - 69^ x = 111^ The correct option is B. 111^. What's next?