Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is:
Question:
Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is:
Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is:
Options
Answer: 36
Explanation:
Step 1: Let daily work of Gautam = G, Suhani = S Together: G + S = 1/20 Step 2: Adjusted work on that special day Gautam: 0.6G Suhani: 1.5S Total = 1 day's usual work: 0.6G + 1.5S = G + S Step 3: Solve for G : S 0.6G + 1.5S = G + S → 0.4G = 0.5S → 4G = 5S → G : S = 5 : 4 Step 4: Find individual rates Let G = 5k, S = 4k → G + S = 9k = 1/20 → k = 1/180 G = 5/180 = 1/36 per day S = 4/180 = 1/45 per day Step 5: Days required by faster worker (Gautam) 1 / (1/36) = 36 days
Explanation:
Step 1: Let daily work of Gautam = G, Suhani = S Together: G + S = 1/20 Step 2: Adjusted work on that special day Gautam: 0.6G Suhani: 1.5S Total = 1 day's usual work: 0.6G + 1.5S = G + S Step 3: Solve for G : S 0.6G + 1.5S = G + S → 0.4G = 0.5S → 4G = 5S → G : S = 5 : 4 Step 4: Find individual rates Let G = 5k, S = 4k → G + S = 9k = 1/20 → k = 1/180 G = 5/180 = 1/36 per day S = 4/180 = 1/45 per day Step 5: Days required by faster worker (Gautam) 1 / (1/36) = 36 days
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