Find the single discount equivalent to three successive discounts of 10%, 20% and 5%.

Exercises · Q12

Q. Find the single discount equivalent to three successive discounts of 10%, 20% and 5%.

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Three successive discounts of $10\%$ , $20\%$ and $5\%$ act one after another, so their retained fractions multiply.

Step 1 — Write the retained fraction after each discount.

1-\frac{10}{100}=0.90,\quad 1-\frac{20}{100}=0.80,\quad 1-\frac{5}{100}=0.95.

Step 2 — Multiply to get the overall factor.

0.90\times0.80=0.72,\qquad 0.72\times0.95=0.684.

So the goods sell for $68.4\%$ of the marked price.

Step 3 — Read off the single equivalent discount.

$\text{Single equivalent}=100\%-68.4\%=31.6\%.$ …

Q.Find the single discount equivalent to three successive discounts of 10%, 20% and 5%.