Question

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 1

(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.