To find a single equivalent discount for successive discounts of 18%, 6%, and 25%, we use the formula for successive discounts:
- Let the successive discounts be \(d_1 = 18\%\), \(d_2 = 6\%\), and \(d_3 = 25\%\).
- The equivalent single discount \(D\) can be calculated using the formula: \(D = d_1 + d_2 + d_3 - \frac{d_1 \cdot d_2}{100}- \frac{d_1 \cdot d_3}{100}- \frac{d_2 \cdot d_3}{100}+ \frac{d_1 \cdot d_2 \cdot d_3}{10000}\)
Substituting the given values:
- Calculate \(d_1 + d_2 + d_3 = 18 + 6 + 25 = 49\%\)
- Calculate \(\frac{d_1 \cdot d_2}{100} = \frac{18 \cdot 6}{100} = 1.08\%\)
- Calculate \(\frac{d_1 \cdot d_3}{100} = \frac{18 \cdot 25}{100} = 4.5\%\)
- Calculate \(\frac{d_2 \cdot d_3}{100} = \frac{6 \cdot 25}{100} = 1.5\%\)
- Calculate \(\frac{d_1 \cdot d_2 \cdot d_3}{10000} = \frac{18 \cdot 6 \cdot 25}{10000} = 0.27\%\)
Now use these to find the equivalent discount:
- Calculate \(D = 49 - 1.08 - 4.5 - 1.5 + 0.27\)
- Simplifying, we get: \(D = 42.19\%\)
Therefore, the single equivalent discount for the successive discounts is 42.19%.
Hence, the correct answer is 42.19%.
Important Questions from Successive Selling
- During a sale 35% of the goods are sold at 22% profit, 40% of the remaining goods are sold at 37% profit and the still remaining goods are sold at a loss of 38%. If there is an overall profit of x%, then what is the value of x?
- A dealer buys two articles X and Y for ₹1,000 each. He marks each of them at the same price. He sells X by giving two successive discounts of 15% and 30% and still earns ₹337 as profit. If he sells Y at a single discount of 49%, then what is the profit percentage on Y?
A shopkeeper marks the price of three identical articles, first, 60% above the Cost Price; second, 45% above the Cost Price and the third, 40% above the cost price. If he gives discount of 25% on first article, 20% on the second article and 15% on the third one, what is his overall profit percentage?
A dealer bought a six-seater Dining Table after getting successive discounts of 15% and 12%. Thereafter, he spent 10% on transport, etc. and finally sold it for Rs. 24,169.75, thereby earning a profit of 25%. What was the marked price of the Dining Table?
A manufacturer sells a product to a wholesaler at a profit of 40%. The wholesaler, in turn, sells it to a retailer at a profit of 60%, and the retailer sells it to a customer at a profit of 25%. If the customer pays ₹714, find the cost price (in) for the manufacturer.
