Question
‘P’ began a business by investing Rs. 24000. After
(x + 2) months, ‘Q’ entered with Rs. 18000, and again after (x + 2) more months, ‘R’ joined them by investing Rs. 30000. If the profit-sharing ratio among them at the end of the year was 8:6:5 respectively, then after how many months from the beginning did ‘R’ join?Solution
ATQ, Let x be the number of months after which Q joined. P: ₹24000 for 12 months → ₹24000 × 12 = 288000 Q: ₹18000 for (12 − x − 2) = 10 − x months → ₹18000 × (10 − x) R: ₹30000 for (12 − 2x − 4) = 8 − 2x months → ₹30000 × (8 − 2x) Given profit ratio: P : Q : R = 8 : 6 : 5 Use Q : R = 6 : 5 18000(10 - x)/30000(8 - 2x) = 6/5 = 3(10 - x )/5(8 - 2x) = 6/5 = 3(10 - x) = 6(8 - 2x) = 30 - 3x = 48 - 12x = x = 2 Then, R joined after: 2x + 4 = 2(2) + 4 = 8 months
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