5 kg of tea and 8 kg of sugar together cost ₹ 172. The price of tea has risen by 20\% and that of sugar by 10\%. Hence the same quantities of tea and sugar now cost ₹ 199.20. What is the original price of tea per kg?
(a)₹ 16
(b)₹ 18
(c)₹ 19
(d)₹ 20
Answer
Answer (as printed): D
Explanation
Let the original price of tea be ₹ $x$ per kg and that of sugar be ₹ $y$ per kg. Then, $5 x+8 y=172 \Rightarrow 15 x+24 y=516$ And, $120 \%$ of $5 x+110 \%$ of $8 y=199.20$ $$\Rightarrow 600 x+880 y=19920 \Rightarrow 15 x+22 y=498$$ Subtracting (ii) from (i), we get: $2 y=18$ or $y=9$. Putting $y=9$ in (i), we get: $x=20$.
Explanation as extracted from the printed page; notation may be imperfect.