Question

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 what I had paid. What per cent of the total amount paid by me was paid for the pens?

• A. 37.5%
• B. 62.5%
• C. 50%
• D. None of these

Hint:

Set up equations carefully when "half more" or percentage comparisons appear.

Answer 1

The Correct Option is A

Let pen = $x$, pencil = $y$, eraser = $z$.
My payment: $5x + 7y + 4z$. Rajan's payment: $6x + 14y + 8z = 1.5(5x + 7y + 4z)$.
Solving: $6x + 14y + 8z = 7.5x + 10.5y + 6z \Rightarrow -1.5x + 3.5y + 2z = 0$.
From this, $1.5x = 3.5y + 2z$. Proportion for pens: $\frac{5x}{5x+7y+4z}$ simplifies to 37.5%.