The price of item $X$ rises by ₹ 40 per year and that of item $Y$ by ₹ 15 per year. If the price of item $X$ and $Y$ in the year 2002 was ₹ 420 and ₹ 630 respectively, in which year the price of item $X$ will be ₹ 40 more than the price of item $Y$ ?
(a)2010
(b)2011
(c)2012
(d)2013
Answer
Answer (as printed): C
Explanation
Let the given condition be fulfilled $n$ years after 2002. Then, price of item $X$ after $n$ years $=₹(420+40 n)$. price of item $Y$ after $n$ years $=₹(630+15 n)$. $$\begin{aligned} \therefore & 420+40 n=(630+15 n)+40 \\ \Rightarrow & 420+40 n=670+15 n \Rightarrow 25 n=250 \Rightarrow n=10 . \end{aligned}$$ So, the required year is 10 years after 2002 i.e., 2012.
Explanation as extracted from the printed page; notation may be imperfect.