Question : The total cost of a dishwasher and a vacuum cleaner was INR 78,750. The vacuum cleaner was sold at a profit of 37% and the dishwasher at a loss of 23%. If the selling price was the same for both items, then the cost price of the cheaper item was:
Option 1: INR 51,375
Option 2: INR 29,375
Option 3: INR 30,750
Option 4: INR 28,335
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Correct Answer: INR 28,335
Solution : Let the cost price of the dishwater and vacuum cleaner be INR $y$ and INR $x$, respectively. Total cost price of a dishwasher and a vacuum cleaner = INR 78,750 $x$ + $y$ = $78750$-------------------(i) Profit of vacuum cleaner = 37% of $x$ = $0.37x$ Selling price of vacuum cleaner = $x$ + $0.37x$ = $1.37x$ Also, the loss of dishwasher = 23% of $y$ = $0.23y$ So, selling price of dishwasher = $y$ – $0.23y$ = $0.77y$ Since both have the same selling price, ⇒ $1.37x = 0.77y$ From equation (i), ⇒ $1.37(78750-y) = 0.77y$ ⇒ $2.14y =107887.5$ ⇒ $y$ = INR $50414.7 $ So, $x=78750-y= 78750-50414.7=28335.3$ = INR 28,335 approx ⇒ Since the vacuum cleaner is less expensive than the dishwasher. Hence, the correct answer is INR 28,335.
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