Question
'A' and 'B' started a business by investing Rs. '3x' and
Rs. '6x' respectively. Four months later, 'A' withdrew Rs. 500 from his investment whereas 'B' invested Rs. 200 more. If at the end of the year, profit share of 'A' was Rs. 8,000 out of total profit of Rs. 28,000, then find the initial investment of 'B'.Solution
ATQ,
Given: A = ₹3x, B = ₹6x After 4 months: A → 3x−500, B → 6x+200 Total profit = ₹28,000, A’s share = ₹8,000 A : B profit = 8000 : 20000 = 2 : 5 A’s share = (3x×4) + (3x−500)×8 = 36x − 4000 B’s share = (6x×4) + (6x+200)×8 = 72x + 1600 Set ratio: (36x − 4000)/(72x + 1600) = 2/5 Solve: 5(36x − 4000) = 2(72x + 1600) 180x − 20000 = 144x + 3200 36x = 23200 → x = 644.44 B’s initial = 6x = 6 × 644.44 = ₹3867
They also lay claim to being the only brothers to finish first and second in the same race.
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