Question : After allowing a discount of 15%, the value of a washing machine is Rs. 29750. If no discount is allowed, then the shopkeeper gains 12%. The cost price of the washing machine is:
Option 1: Rs. 31250
Option 2: Rs. 31500
Option 3: Rs. 31750
Option 4: Rs. 32000
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Correct Answer: Rs. 31250
Solution :
Selling Price (SP) = Rs. 29750
Discount = 15%
Profit = 12%
Discount = 15% = $\frac{3}{20}$ (fractional equivalent)
Let the marked price be 20$x$.
Then the discount will be 3$x$.
Selling Price = Marked Price – Discount
SP = 20$x$$-$3$x$ = 17$x$
According to the question,
We get 17$x$ = Rs. 29750
⇒ $x$ = $\frac{29,750}{17}$ = 1750
Now, Marked Price (MP) = 20$x$ = 20 × 1750 = Rs. 35000
If MP = SP,
Cost Price (CP) $\times{(\frac{100+Profit\%}{100})}$ = Selling Price = Marked Price
⇒ CP$\times{(\frac{112}{100})}$ = 35,000
⇒ CP = Rs. 31,250
$\therefore$ The cost price of the washing machine is Rs. 31250.
Hence, the correct answer is Rs. 31250.
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