The single discount equivalent to the discount series of 15%, 20% and 5% is:

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Accepted Answer

To find the single equivalent discount for a series of discounts, we use the formula:

Let the discounts be d1 = 15%, d2 = 20%, and d3 = 5%.

Equivalent discount, D = 1 - (1 - d1)(1 - d2)(1 - d3)

Convert percentages to decimals:

d1 = 0.15, d2 = 0.20, d3 = 0.05

Calculate:

(1 - d1) = 1 - 0.15 = 0.85
(1 - d2) = 1 - 0.20 = 0.80
(1 - d3) = 1 - 0.05 = 0.95

Multiply:
0.85 × 0.80 = 0.68
0.68 × 0.95 = 0.646

Now,
D = 1 - 0.646 = 0.354 or 35.4%

Therefore, the single discount equivalent to the series of discounts 15%, 20%, and 5% is 35.4%.

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