1. A and B started a business with initial investments in the respective ratio of 18 : 7. After four months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more. At the end of one year, if the profit was distributed among them in the ratio of 2 : 1 respectively, what was the total initial investment with which A and B started the business?
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By: anil on 05 May 2019 01.37 am
Let amount invested by A = $$Rs. 18x$$ => Amount invested by B = $$Rs. 7x$$ After four months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more Thus, ratio of profit received by A : B = $$[(18x imes 4) + (18x + 2000) imes 8] : [(7x imes 4) + (7x + 7000) imes 8]$$ = $$(72x + 144x + 16000) : (28x + 56x + 56000)$$ = $$(216x + 16000) : (84x + 56000) = (54x + 4000) : (21x + 14000)$$ Acc. to ques, => $$frac{54x + 4000}{21x + 14000} = frac{2}{1}$$ => $$54x + 4000 = 42x + 28000$$ => $$54x - 42x = 12x = 28000 - 4000 = 24000$$ => $$x = frac{24000}{12} = 2000$$ $$ herefore$$ Total initial investment = $$18x + 7x = 25x$$ = $$25 imes 2000 = Rs. 50,000$$
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