Question
P started a business with Rs. 12,600. After 'n' months,
Q joined the business with Rs. 15,600 and P increased his investment by Rs. 1,400. At the end of 18 months, P's share of the profit was Rs. 8,400 out of a total profit of Rs. 15,600. Find the value of 2n.Solution
ATQ,
Ratio of profit share of P to Q = [12,600 × n + 14,000 × (18 - n)] : [15,600 × (18 - n)] = [9n + 10 × (18 - n)] : [12 × (18 - n)] = (180 - n) : (216 - 12n) So, (180 - n) : (216 - 12n) = 8,400 : (15,600 - 8,400) Or, (180 - n) : (216 - 12n) = 8,400 : 7,200 Or, (180 - n) : (18 - n) = 7 : 6 Or, 180 - n = 210 - 7n Or, 6n = 30 Or, n = 5 Therefore, required value = 2 × 5 = 10
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