A profit of 10% is made when a smartphone is sold for P rupees, while a loss…

Concept

For the same cost price C, the selling price is C(1 + r/100) at r% profit and C(1 - l/100) at l% loss. Therefore, the ratio of two selling prices equals the ratio of their percentage multipliers.

Application

1. Let the cost price of the smartphone be C rupees.

2. At 10% profit, P = C(1 + 10/100) = 1.10C = 110C/100.

3. At 4% loss, Q = C(1 - 4/100) = 0.96C = 96C/100.

4. Thus P:Q = (110C/100):(96C/100) = 110:96 = 55:48.

5. The listed ratios 110:96 and 55:48 denote the same relationship, so more than one listed numerical ratio represents P:Q.

Cross-check

1. Take C = 100; then P = 110 and Q = 96.

2. Form P:Q = 110:96 and divide both terms by their common factor 2 to obtain 55:48.

3. The direct percentage-multiplier calculation and this numerical substitution give the same two equivalent ratio forms.

Result: More than one of the above.