A luxury smartphone is initially marked up by 70% above its cost price. During a clearance sale, it is offered at a discount of 30% on its marked price. However, a corporate buyer receives an additional discount of w% on the discounted price, bringing the final selling price to ₹56,700. If the shopkeeper still makes a profit of 15.5% on the cost price after all discounts, what was the original cost price of the smartphone and the value of w?

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Accepted Answer

1. Let CP = $x$. Marked price = $1.7x$. After 30% off price = $1.19x$. After extra $w\%$ off final price = $1.19x(1-	frac{w}{100})$.

2. Given final price = ₹56,700 and profit 15.5%, so final = $1.155x$. Equate: $1.19x(1-	frac{w}{100})=1.155x$.

3. Cancel $x$: $1-	frac{w}{100}=	frac{1.155}{1.19}=	frac{231}{238}$. Thus $	frac{w}{100}=	frac{7}{238}$, so $w=	frac{700}{238}\approx2.94\%\approx3\%$.

4. Find CP: $1.155x=56{,}700\Rightarrow x=\dfrac{56{,}700}{1.155}=49{,}090.91\approx49{,}000$. So option (a) is the nearest match.

FINAL_ANSWER: a

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