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.
ScanSolve AI Answer
Step 1: Determine the daily work rate of 10 men. 10 men can complete the work in 15 days. So, in 1 day, 10 men complete (1)/(15) of the work. Step 2: Determine the daily work rate of 15 women. 15 women can complete the work in 12 days. So, in 1 day, 15 women complete (1)/(12) of the work. Step 3: Calculate the combined daily work rate of 10 men and 15 women. When working together, their daily work rates add up. Combined daily work rate = (1)/(15) + (1)/(12) Step 4: Add the fractions by finding a common denominator. The least common multiple (LCM) of 15 and 12 is 60. (1)/(15) + (1)/(12) = (1 × 4)/(15 × 4) + (1 × 5)/(12 × 5) = (4)/(60) + (5)/(60) = (4+5)/(60) = (9)/(60) Step 5: Simplify the combined daily work rate. (9)/(60) = (9 ÷ 3)/(60 ÷ 3) = (3)/(20) So, 10 men and 15 women together complete (3)/(20) of the work in 1 day. Step 6: Calculate the total number of days to complete the entire work. If they complete (3)/(20) of the work in 1 day, then the total time to complete the work is the reciprocal of their daily work rate. Time taken = (1)/(3)20 = (20)/(3) days. Step 7: Convert the improper fraction to a mixed number. (20)/(3) = 6 (2)/(3) days Comparing this with the given options: a) 6 (2)/(3) days b) 8 (1)/(3) days c) 7 (2)/(3) days d) None of these The calculated answer matches option a). The final answer is a) 6 (2)/(3) days. Send me the next one 📸