The cash difference between the selling prices of an article at a profit of $$4 \%$$ and $$6 \%$$ is Rs. $$3$$. The ratio of the two selling prices is.
Correct option is D. $$52:53$$
Let cost price (CP) of the article be X rs.
For $$4\%$$ profit, $$SP=CP+4\%\ of\ CP=1.04X$$
For $$6\%$$ profit, $$SP=CP+6\%\ of\ CP=1.06X$$
It is given that cash differences between selling price is Rs $$3$$
$$\Rightarrow 1.06X-1.04X=3$$
$$\Rightarrow 0.02X=3$$
$$\therefore X=150$$
i.e. Selling price of first article $$=1.04X=1.04\times 150=156\ Rs$$
and Selling price of second article $$=1.06X=1.06\times 150=159\ Rs$$
$$\therefore$$ Ratio of selling prices $$=\dfrac{156}{159}=52:53$$