On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs 7.

1.	On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs 7. If he sell the pen at 5% gain and the book at 10% gain, then he gains Rs 13. The actual price of the book is (a) Rs 100 (b) Rs 80(c) Rs 10 (d) Rs 400
Answer» (b) Rs 80 Let the cost price of the pen and the book be Rs x and Rs y respectively. Case I: When the pen is sold at 5% loss and book at 15% gain, Loss on pen =Rs \(\frac{5X}{100}\) = Rs \(\frac{X}{20}\) Gain on book = Rs \(\frac{15y}{100}\) = Rs \(\frac{3y}{20}\) \(\therefore\) Net gain = Rs \(\frac{3y}{20}\)- Rs \(\frac{X}{20}\) Given, \(\frac{3y}{20}\) - \(\frac{X}{20}\) = 7 \(\Rightarrow\) 3y -x =140 ..........(i) Case II: When the pen is sold at 5% gain and book at 10% gain Gain on pen = Rs \(\frac{5X}{100}\)= Rs \(\frac{X}{20}\) Gain on book = Rs \(\frac{10y}{100}\) = Rs \(\frac{y}{10}\) \(\therefore\) Net gain = \(\frac{X}{20}\) + \(\frac{y}{10}\) Given, \(\frac{X}{20}\) + \(\frac{y}{10}\) = 13 \(\Rightarrow\) x + 2y = 260 ......…(ii) Now, solve equation (i) and (ii) for the value of x and y.

On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs 7. If he sell the pen at 5% gain and the book at 10% gain, then he gains Rs 13. The actual price of the book is (a) Rs 100 (b) Rs 80(c) Rs 10 (d) Rs 400

Answer»

(b) Rs 80

Let the cost price of the pen and the book be Rs x and Rs y respectively.

Case I: When the pen is sold at 5% loss and book at 15% gain,

Loss on pen =Rs \(\frac{5X}{100}\) = Rs \(\frac{X}{20}\)

Gain on book = Rs \(\frac{15y}{100}\) = Rs \(\frac{3y}{20}\)

\(\therefore\) Net gain = Rs \(\frac{3y}{20}\)- Rs \(\frac{X}{20}\)

Given, \(\frac{3y}{20}\) - \(\frac{X}{20}\) = 7

\(\Rightarrow\) 3y -x =140 ..........(i)

Case II: When the pen is sold at 5% gain and book at 10% gain

Gain on pen = Rs \(\frac{5X}{100}\)= Rs \(\frac{X}{20}\)

Gain on book = Rs \(\frac{10y}{100}\) = Rs \(\frac{y}{10}\)

\(\therefore\) Net gain = \(\frac{X}{20}\) + \(\frac{y}{10}\)

Given, \(\frac{X}{20}\) + \(\frac{y}{10}\) = 13

\(\Rightarrow\) x + 2y = 260 ......…(ii)

Now, solve equation (i) and (ii) for the value of x and y.