Recognize this as an inverse proportion problem. More boys will take less time to load the same amount of cement.

Here are the solutions to the problems: 20. 2 boys can load a lorry of cement in 6hrs. How long will it take 5 such boys to load the same lorry of cement? Step 1: Recognize this as an inverse proportion problem. More boys will take less time to load the same amount of cement. Let B be the number of boys and T be the time in hours. The product B × T is constant. B_1 T_1 = B_2 T_2 Step 2: Substitute the given values. B_1 = 2 boys, T_1 = 6 hours B_2 = 5 boys, T_2 = ? 2 × 6 = 5 × T_2 Step 3: Solve for T_2. 12 = 5 T_2 T_2 = (12)/(5) T_2 = 2.4 It will take 5 boys 2.4 hours to load the same lorry of cement. 21. A tank of water of capacity 5000 litres serves a family for 16 days. How long will it take a water tank of 8000 litres to serve the same family? Step 1: Recognize this as a direct proportion problem. A larger capacity tank will serve the family for more days. Let C be the capacity in litres and D be the number of days. The ratio (C)/(D) is constant. (C_1)/(D_1) = (C_2)/(D_2) Step 2: Substitute the given values. C_1 = 5000 litres, D_1 = 16 days C_2 = 8000 litres, D_2 = ? (5000)/(16) = (8000)/(D_2) Step 3: Solve for D_2. 5000 D_2 = 8000 × 16 5000 D_2 = 128000 D_2 = (128000)/(5000) D_2 = (128)/(5) D_2 = 25.6 A water tank of 8000 litres will serve the same family for 25.6 days. 22. 9 men working at the same rate and working 8 hrs in a day take 12 days to complete a given task. How long will it take six such men working 10 hrs in a day to complete the same task? Step 1: Recognize this as a compound proportion problem. The total work done is constant. Let M be the number of men, H be the hours worked per day, and D be the number of days. The total work units can be represented as M × H × D. M_1 H_1 D_1 = M_2 H_2 D_2 Step 2: Substitute the given values. M_1 = 9 men, H_1 = 8 hours/day, D_1 = 12 days M_2 = 6 men, H_2 = 10 hours/day, D_2 = ? 9 × 8 × 12 = 6 × 10 × D_2 Step 3: Calculate the total work units for the first scenario. 9 × 8 × 12 = 72 × 12 = 864 Step 4: Set up the equation for the second scenario and solve for D_2. 864 = 60 D_2 D_2 = (864)/(60) D_2 = (144)/(10) D_2 = 14.4 It will take six men working 10 hours a day 14.4 days to complete the same task. 23. What is the order of the matrix below? 7 & -1 \\ -2 & 3 \\ 9 & 4 Step 1: Count the number of rows. There are 3 rows. Step 2: Count the number of columns. There are 2 columns. Step 3: State the order as (number of rows) × (number of columns). The order of the matrix is 3 × 2. 24. Are the matrices below compatible? 2 & 3 \\ 4 & 9 - 3 & 9 & -2 \\ 4 & 6 & 4 \\ 1 & 3 & 8 Step 1: Determine the order of the first matrix. It has 2 rows and 2 columns, so its order is 2 × 2. Step 2: Determine the order of the second matrix. It has 3 rows and 3 columns, so its order is 3 × 3. Step 3: Check for compatibility for subtraction. For matrix addition or subtraction, the matrices must have the exact same order. Since the orders (2 × 2 and 3 × 3) are different, the matrices are not compatible for subtraction. The matrices are not compatible. 25. Work out 6 & 6 \\ 3 & -7 \\ 4 & 10 + 0 & 9 \\ 1 & 6 \\ -2 & -8 Step 1: Perform matrix addition by adding corresponding elements. 6+0 & 6+9 \\ 3+1 & -7+6 \\ 4+(-2) & 10+(-8) Step 2: Simplify each element. 6 & 15 \\ 4 & -1 \\ 2 & 2 The result of the addition is 6 & 15 \\ 4 & -1 \\ 2 & 2 . 26. Given A=B-C and A = 2 & 0 & 3 \\ 4 & -1 & 7 \\ 6 & 3 & 9 B = 3 & 6 & 9 \\ -1 & 0 & 4 \\ 4 & 2 & 6 Step 1: Rearrange the equation to solve for C. Given A = B - C, we can write C = B - A. Step 2: Substitute the given matrices A and B into the equation for C. C = 3 & 6 & 9 \\ -1 & 0 & 4 \\ 4 & 2 & 6 - 2 & 0 & 3 \\ 4 & -1 & 7 \\ 6 & 3 & 9 Step 3: Perform matrix subtraction by subtracting corresponding elements. C = 3-2 & 6-0 & 9-3 \\ -1-4 & 0-(-1) & 4-7 \\ 4-6 & 2-3 & 6-9 Step 4: Simplify each element. C = 1 & 6 & 6 \\ -5 & 1 & -3 \\ -2 & -1 & -3 The matrix C is 1 & 6 & 6 \\ -5 & 1 & -3 \\ -2 & -1 & -3 . That's 2 down. 3 left today — send the next one.