I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than that I had paid. What percent of the total amount paid by me was paid for the pen?
(a)37.5\%
(b)50\%
(c)62.5\%
(d)None of these
Answer
Answer (as printed): C
Explanation
Let the individual cost of 1 pen, 1 pencil and 1 eraser be ₹ $x$, ₹ $y$ and ₹ $z$ respectively. $$\begin{aligned} & \text { Then, } 5 x+7 y+4 z=p \quad \text { (say) } \\ & \text { And, } 6 x+14 y+8 z=1.5 p \end{aligned}$$ Multiplying (i) by 2 and subtracting (ii) from it, we get: $4 x=0.5 p$ or $x=0.125 p$. $$\therefore \quad \text { Required percentage }=\left(\frac{0.625 p}{p} \times 100\right) \%=62.5 \% .$$
Explanation as extracted from the printed page; notation may be imperfect.