P and Q invested some money in a business in the ratio of 4 : 7 respectively. After 6 months P withdraws his capital. If they receive profits in the ratio of 4 : 21, then for how many months did Q invest in the business?
Let P invested Rs. 4 for 6 months and Q invested Rs. 7 for $$x$$ months
=> Ratio of profits of P:Q = $$(4\times6):(7\times x)$$
According to ques,
=> $$\frac{24}{7x}=\frac{4}{21}$$
=> $$7x\times4=24\times21$$
=> $$x=\frac{24\times21}{7\times4}$$
=> $$x=6\times3=18$$ months
=> Ans - (C)
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