Question

A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he would have made a 10% gain. What is the loss in Rupees incurred by the fruit seller?
1. 48
2. 52
3. 60
4. 108

Answer 1

Correct Answer - Option 3 : 60

\({\rm{Loss\;}}12.5{\rm{\% }} = \frac{{12.5}}{{100}} = \frac{1}{8}\)

\({\rm{Multiplying\;factor\; (f_1)}}=\frac{{\left( {{\rm{SP}} } \right)}}{{{\rm{CP}}}}= 1 - \frac{1}{8} = \frac{7}{8}\)

\({\rm{Profit\;}}10{\rm{\% }} = \frac{{10}}{{100}} = \frac{1}{{10}}\)

\({\rm{Multiplying\;factor}} =\frac{{\left( {{\rm{SP}} + 108} \right)}}{{{\rm{CP}}}}= 1 + \frac{1}{{10}} = \frac{{11}}{{10}}\)

As per given condition,

Selling price (SP) and cost price (CP)

\(\frac{{{\rm{SP}}}}{{{\rm{CP}}}} = {{\rm{f}}_1} = \frac{7}{8},\frac{{\left( {{\rm{SP}} + 108} \right)}}{{{\rm{CP}}}} = {{\rm{f}}_2} = \frac{{11}}{{10}},\)

\(\frac{{{\rm{SP}}}}{{{\rm{CP}}}} + \frac{{108}}{{{\rm{CP}}}} = \frac{{11}}{{10}} \Rightarrow \frac{{108}}{{{\rm{CP}}}} = \frac{{11}}{{10}} - \frac{{{\rm{SP}}}}{{{\rm{CP}}}}\)

\(\frac{{108}}{{{\rm{CP}}}} = \frac{{11}}{{10}} - \frac{7}{8}\)

\(\frac{{108}}{{{\rm{CP}}}} = \frac{9}{{40}} \Rightarrow {\rm{CP}} = \frac{{108 \times 40}}{9} = 480\)

\({\rm{Loss\;in\;Rs}}.{\rm{\;}} = {\rm{CP}} \times {\rm{Loss\% }} = 480 \times \frac{{12.5}}{{100}} = {\rm{Rs}}.{\rm{\;}}60\)