Multiple choice

Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it? चार पुरुष और तीन महिलाएं कोई कार्य 6 दिनों में कर सकते हैं। जब पांच पुरुष और छह महिलाएं समान कार्य करती हैं, तो कार्य 4 दिनों में पूरा हो जाता है। यदि कोई महिला अकेले काम करती है, तो कार्य करने में कितना समय लगेगा?

  1. 38 days/दिन

  2. 54 days/दिन

  3. 44 days/दिन

  4. 56 days/दिन
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B Correct answer
Explanation

Let m = one man's daily work, w = one woman's daily work. 4m + 3w = 1/6 (work per day). 5m + 6w = 1/4. Subtracting: (5m+6w) - (4m+3w) = m + 3w = 1/4 - 1/6 = 1/12. Substituting m = 1/12 - 3w in first equation: 4(1/12-3w) + 3w = 1/6, giving w = 1/54. So one woman takes 54 days. This requires solving simultaneous equations for work rates.

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