A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements :
1. The work will be finished on Thursday.
2. The work will be finished in 10 days.
Which of the above statements is/are correct ?
The correct answer is (A) 1 only.
Explanation:
Let's analyze the work rates of A, B, and C: A can do the work in 8 days (1/8 per day). B can do the work in 16 days (1/16 per day). C can do the work in 12 days (1/12 per day). They work in a rotating cyclic order: Mon (A), Tue (B), Wed (C), Thu (A), Fri (B), Sat (C), Sun (A), Mon (B), Tue (C), Wed (A)... Let's calculate the work done in a 3-day cycle (A + B + C): Work in 1 cycle = (1/8) + (1/16) + (1/12). LCM of 8, 16, 12 is 48. Work = (6/48) + (3/48) + (4/48) = 13/48 of the work per 3-day cycle. Let's track work over multiple cycles: After 3 cycles (9 days): Work done = 3 × (13/48) = 39/48. Remaining work = 48/48 - 39/48 = 9/48. On the 10th day (Thursday), it's A's turn. A's 1-day work is 6/48. Remaining work after Thursday = 9/48 - 6/48 = 3/48. On the 11th day (Friday), it's B's turn. B's 1-day work is 3/48. B finishes the remaining 3/48 on Friday! Therefore, the work finishes on Friday, taking 11 days in total. Let's check the given statements: 1. The work will be finished on Thursday. (False, it finishes on Friday). 2. The work will be finished in 10 days. (False, it takes 11 days). Thus, neither statement 1 nor statement 2 is correct.
हिंदी में प्रश्न एवं आदर्श उत्तर
A, B, C अलग-अलग काम करते हुए किसी काम को क्रमशः 8, 16 और 12 दिनों में पूरा कर सकते हैं । अकेला A सोमवार को काम करता है, अकेला B मंगलवार को काम करता है, अकेला C बुधवार को काम करता है; A फिर से अकेला बृहस्पतिवार को काम करता है और इसी तरह यह क्रम जारी रहता है । निम्नलिखित कथनों पर विचार कीजिए :
1. यह काम बृहस्पतिवार को पूरा हो जाएगा ।
2. यह काम 10 दिनों में पूरा हो जाएगा ।
उपर्युक्त कथनों में से कौन-सा/से सही है/हैं ?
सही उत्तर (A) 1 only है।
व्याख्या:
Let's analyze the work rates of A, B, and C: A can do the work in 8 days (1/8 per day). B can do the work in 16 days (1/16 per day). C can do the work in 12 days (1/12 per day). They work in a rotating cyclic order: Mon (A), Tue (B), Wed (C), Thu (A), Fri (B), Sat (C), Sun (A), Mon (B), Tue (C), Wed (A)... Let's calculate the work done in a 3-day cycle (A + B + C): Work in 1 cycle = (1/8) + (1/16) + (1/12). LCM of 8, 16, 12 is 48. Work = (6/48) + (3/48) + (4/48) = 13/48 of the work per 3-day cycle. Let's track work over multiple cycles: After 3 cycles (9 days): Work done = 3 × (13/48) = 39/48. Remaining work = 48/48 - 39/48 = 9/48. On the 10th day (Thursday), it's A's turn. A's 1-day work is 6/48. Remaining work after Thursday = 9/48 - 6/48 = 3/48. On the 11th day (Friday), it's B's turn. B's 1-day work is 3/48. B finishes the remaining 3/48 on Friday! Therefore, the work finishes on Friday, taking 11 days in total. Let's check the given statements: 1. The work will be finished on Thursday. (False, it finishes on Friday). 2. The work will be finished in 10 days. (False, it takes 11 days). Thus, neither statement 1 nor statement 2 is correct.