\(A\) and \(B\) invest in a business in the ratio \(3: 2\). If \(5 \%\) of the total profit goes to charity and \(A\) 's share is \(\$ 855\), the total profit is ____________
A. \(\$ 1425\) B. \(\$ 1500\) C. \(\$ 1537.50\) D. \(\$ 1576\) E. \(\$ 1640\)
Correct Answer: B
Explanation
Say \(\mathrm{P}\) is the total profit and \(5 \%\) of \(\mathrm{P}\) goes to charity. \(\Rightarrow 95 \%\) of \(P\) is to be shared between \(A\) and \(B\) in the ratio \(3: 2\) \(\Rightarrow\) A's share of profit is \(3 / 5\) of \(95 \%\) of \(P\) \(\Rightarrow 855=(3 / 5) \times 0.95 \times \mathrm{P}\) \(\Rightarrow P=(855 \times 5) \div(3 \times 0.95)=\$ 1500\)
