Multiple choice

Few man can do a piece of work in 8 day. Then start the work but every day 10 men left the work the work will be completed in 12 days. find the number of men at the starting. कुछ व्यक्ति किसी काम को 8 दिनों में कर सकते है। वे एक साथ काम आरम्भ करते है परन्तु प्रतिदिन 10 आदमी काम छोड़ कर चले जाते है तो काम 12 दिनों में पूरा हो जाता है। तो आरम्भ में कितने व्यक्ति थे।

  1. 175

  2. 165

  3. 185

  4. 195

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the initial number of men. Each day, 10 men leave, so on day i, n - 10(i-1) men work. Total work = n × 8 (since n men complete work in 8 days). The work equation: n + (n-10) + (n-20) + ... + (n-110) = 8n (12 terms, last term n-110). Sum = 12n - 10(0+1+...+11) = 12n - 10 × 66 = 12n - 660. So 12n - 660 = 8n, giving 4n = 660, so n = 165.