A shop runs a "Buy 4, Get b Free" scheme and also gives a trade discount of 20%. If the overall effective discount to the customer is 46 2/3%, what is the value of b?
2
Let the marked price of one item be ₹1. Under "Buy 4, Get b Free", the customer pays for 4 items but receives 4 + b items.
With the further 20% trade discount, the customer pays 4 × 0.8 = ₹3.2 for goods worth ₹(4 + b).
Effective discount = \(1 - \frac{3.2}{4 + b}\), and this equals \(46\frac{2}{3}\% = \frac{7}{15}\), so \(\frac{3.2}{4 + b} = \frac{8}{15}\).
So \(4 + b = \frac{3.2 \times 15}{8} = 6\), which gives b = 2.
Check: with b = 2 the customer gets 6 items worth ₹6 for ₹3.2; the saving is ₹2.8, and \(\frac{2.8}{6} \times 100 = 46\frac{2}{3}\%\), as given.
Hence, 2.
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