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let she invested $a per day to purchase shares for the 3 days i.e. total cost price=$3a and profit is 15%.
so total no. of shares purchased in 3 days =(a/3 + a/4 + a/x)
selling price of the shares=4.6(a/3 + a/4 + a/x) = 3a*1.15
7/12+1/x=3/4
1/x=1/6
x=6
E
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Another way to look at this question is of mixing three quantities with cost price.. We are given the mixture selling price.
Find the mixture cost price = 4.6/1.15 = 4.

Amount is same in all. Number of shares would be --> 1/3 + 1/4 + 1/x = 3/4.

x = 6
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