# CAT2019-1: 70

1 vote
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On selling a pen at $5$% loss and a book at $15$% gain, Karim gains Rs. $7$. If he sells the pen at $5$% gain and the book at $10$% gain, he gains Rs. $13$. What is the cost price of the book in Rupees?

1. $80$
2. $85$
3. $95$
4. $100$

edited

Cost price of Pen – $\text{100 x}$

Cost price of Book – $\text{100 y}$

$\because$ On selling a pen at $5\%$ loss.

Selling a book at $15\%$ gain.

He gains $7$ Rupees.

So, equation will be :-

$\require{cancel} \begin{array} { c c } \text{Pen} & \text{ Book} \\ 100\:x\times \frac{-5}{100} & 100\:y\times \frac{15}{\cancel{100}} \end{array}$

$\boxed{-5x+15y = Rs\:7} \to (i)$

If he sells the pen at $5\%$ gain

If he sells the book at $10\%$ gain

He gain $13$ rupees.

So, equation will be :-

$\require{cancel} \begin{array} { c c } \text{Pen} & \text{ Book} \\ 100\:x\times \frac{+5}{100} & 100\:y\times \frac{10}{100} \end{array}$

$\boxed{+5x+10y = Rs\:13} \to (ii)$

Equating both we get,

$\begin{matrix} {\cancel{-5x}} +15y =7\to (i) \\ \underline{{\cancel{-5x}} +10y =13}\to (ii)\\ \implies 25y=20 \end{matrix}\\ \implies\boxed{y=\frac{20}{25}}$

Cost price of Book – $\text{100 y}$

$\implies100\times\frac{20}{25}$

$\implies 80$

$\therefore$ so cost price of book is Rs $80$.

498 points 1 2 5
edited

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