Question
A and B together can complete a work in 10 days, B and C
together in 12 days and C and A together in 15 days. In how many days can each of them complete the work alone?Solution
Let daily work rates be a, b, c. a + b = 1/10 b + c = 1/12 c + a = 1/15 Add all three: 2(a + b + c) = 1/10 + 1/12 + 1/15 LCM(10,12,15) = 60 1/10 = 6/60, 1/12 = 5/60, 1/15 = 4/60 Sum = 15/60 = 1/4 ⇒ a + b + c = 1/8 Now: a = (a + b + c) − (b + c) = 1/8 − 1/12 = 3/24 − 2/24 = 1/24 ⇒ A alone: 24 days b = (a + b + c) − (a + c) = 1/8 − 1/15 = 15/120 − 8/120 = 7/120 ⇒ B alone: 120/7 days c = (a + b + c) − (a + b) = 1/8 − 1/10 = 5/40 − 4/40 = 1/40 ⇒ C alone: 40 days.
Statements: All shoes are leather. Some leather are belts. Some belts are gold.
Conclusion I: Some shoes are belts.
Conclusion II: All belts are gold.
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