A trader mixes tea worth Rs 200 per kg with tea worth Rs 300 per kg to make 20 kg of a blend worth Rs 4600 in all. How many kilograms of the cheaper tea does he use?

Let $x$ kg of the cheaper tea and $y$ kg of the costlier be mixed. $x+y=20$ and $200x+300y=4600$. Substituting $y=20-x:200x+6000-300x=4600$, so $100x=1400$ and $x=14$, giving $y=6$. Check: 14 + 6 = 20 and 2800 + 1800 = 4600. 6 kg is the costlier tea; 10 kg assumes an equal split; 16 kg follows from a sign slip in the elimination, and 16 kg with 4 kg is worth 3200 + 1200 = Rs 4400, not Rs 4600.