1950 AHSME Problems/Problem 22

Problem

Successive discounts of $10\%$ and $20\%$ are equivalent to a single discount of:

$\textbf{(A)}\ 30\%\qquad\textbf{(B)}\ 15\%\qquad\textbf{(C)}\ 72\%\qquad\textbf{(D)}\ 28\%\qquad\textbf{(E)}\ \text{None of these}$

Solution 1 (Kind of Lame)

Without loss of generality, assume something costs $100$ dollars. Then with each successive discount, it would cost $90$ dollars, then $72$ dollars. This amounts to a total of $28$ dollars off, so the single discount would be $\boxed{\mathrm{(D)}\ 28\%.}$

Solution 2 (Technical)

Let the object cost $x$ dollars. After the $10\%$ discount, it's worth $(1-10\%)x=0.9x$ dollars. After a $20\%$ discount on that, it's worth $(1-20\%)(0.9x)=0.72x$ dollars. Say the single discount is of $k$ . Then $(1-k)x=0.72x$ . So $k=0.28$ , or $k=28\%$ . So select $\boxed{D}$ .

~hastapasta

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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1950 AHSME Problems/Problem 22

Contents

Problem

Solution 1 (Kind of Lame)

Solution 2 (Technical)

See Also