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Rectangular solid $A$ has a length $15 \%$ longer than the length of r
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30 Oct 2025, 23:45
30 Oct 2025, 23:45
Expert Reply
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Rectangular solid $\(A\)$ has a length $15 %$ longer than the length of rectangular solid $\(B\)$, and a width that is $60 %$ shorter. Both solids have the same height. What is the ratio of solid A's volume to the volume of solid $\(B\)$ ?
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\(\frac{23}{50}\)
Re: Rectangular solid $A$ has a length $15 \%$ longer than the length of r
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08 Nov 2025, 10:09
08 Nov 2025, 10:09
Expert Reply
In order to solve this problem, we do not need to know the exact values of solid A's dimensions. Because we're just looking for a ratio, we need to know only how the two solids' dimensions differ.
Solid $B$ 's dimensions are $l, w$, and $h$.
Solid $A$ 's dimensions: its length is $15 %$ longer, or 1.15; its width is $60 %$ shorter, or $100 %-60 %=40 %$ of $B$ 's width: $0.4 w$; and its height is the same.
So Solid $A$ 's dimensions are $1.15 , 0.4 w$, and $h$.
To figure out the volumes, we just multiply all three dimensions together.
Solid $B$ volume $\(=v=I w h\)$
Solid $A$ volume $\(=v=(1.15)(0.4)(1 w h)=\)$ (0.46)/wh
Now we can figure out the ratio of volumes between $A$ and $B$.
$$
\(\begin{gathered}
(0.46) / w h: / w h=\frac{0.46}{1}=0.46 \\
\frac{46}{100}=\frac{23}{50}
\end{gathered}\)
$$
Solid $B$ 's dimensions are $l, w$, and $h$.
Solid $A$ 's dimensions: its length is $15 %$ longer, or 1.15; its width is $60 %$ shorter, or $100 %-60 %=40 %$ of $B$ 's width: $0.4 w$; and its height is the same.
So Solid $A$ 's dimensions are $1.15 , 0.4 w$, and $h$.
To figure out the volumes, we just multiply all three dimensions together.
Solid $B$ volume $\(=v=I w h\)$
Solid $A$ volume $\(=v=(1.15)(0.4)(1 w h)=\)$ (0.46)/wh
Now we can figure out the ratio of volumes between $A$ and $B$.
$$
\(\begin{gathered}
(0.46) / w h: / w h=\frac{0.46}{1}=0.46 \\
\frac{46}{100}=\frac{23}{50}
\end{gathered}\)
$$
gmatclubot
Re: Rectangular solid $A$ has a length $15 \%$ longer than the length of r [#permalink]
08 Nov 2025, 10:09
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