Question
Download Solution PDFA, B, and C started a business. A invested Rs. x, B invested Rs. (x+1000), and C invested Rs. 8000. Their investments were for 5 months, 5 months, and 12 months respectively. If the total profit at the end of the year was Rs. 3800 and the profit share of B was Rs. 500,
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFA's investment = x for 5 months ⇒ A's share = x × 5 = 5x
B's investment = (x + 1000) for 5 months ⇒ B's share = 5(x + 1000)
C's investment = 8000 for 12 months ⇒ C's share = 8000 × 12 = 96000
Total profit = Rs. 3800
B’s profit = Rs. 500
⇒ B's share / Total share = 500 / 3800 = 5 / 38
B’s ratio = 5(x + 1000)
Total ratio = 5x + 5(x + 1000) + 96000 = 5x + 5x + 5000 + 96000 = 10x + 101000
⇒ B’s share / Total share = 5(x + 1000) / (10x + 101000)
⇒ 5(x + 1000) / (10x + 101000) = 5 / 38
⇒ 38 × 5(x + 1000) = 5 × (10x + 101000)
⇒ 190(x + 1000) = 5(10x + 101000)
⇒ 190x + 190000 = 50x + 505000
⇒ 190x - 50x = 505000 - 190000
⇒ 140x = 315000
⇒ x = 315000 ÷ 140 = 2250
Thus, the correct answer is Rs. 2250.
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