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 then he gains Rs. $13$ . The actual price of the book is :

Rs.

100

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Rs.

80

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Rs.

10

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Rs.

400

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Solution

The correct option is B Rs. $80$
Let the C.P. of the pen be Rs. $x$ and C.P. of he book be Rs. $y$ .
Then S.P. of pen at $5 %$ loss $= x \times \frac{95}{100} = R S . \frac{95 x}{100}$
S.P. of book at $15 %$ gain $= y \times \frac{115}{100} =$ Rs. $\frac{115 y}{100}$
Given, $(\frac{95 x}{100} - x) + (\frac{115 y}{100} - y) = 7$
$\Rightarrow - 5 x + 15 y = 700$
$\Rightarrow - x + 3 y = 140$ or $x - 3 y = - 140$ ..........(i)
Again S.P. of pen at $5 %$ gain $=$ $x \times \frac{105}{100} = \frac{105 x}{100}$
S.P. of book at $10 %$ gain $=$ $y \times \frac{110}{100} = \frac{110 y}{100}$
Given, $(\frac{105 x}{100} - x) + (\frac{110 y}{100} - y) = 13$
$\Rightarrow 5 x + 10 y = 1300$
$\Rightarrow x + 2 y = 260$ .........(ii)
Subtracting eqn. (i) from eqn (ii), we get
$(x + 2 y) - (x - 3 y) = 260 + 140$
$\Rightarrow$ $5 y = 400$
$\Rightarrow$ $y = 80$
Thus, the actual price of the book is Rs. $80$ .

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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 then he gains Rs. 13. The actual price of the book is :

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 then he gains Rs. $13$ . The actual price of the book is :