Lily is $90 \mathrm{~cm}$ tall. If Anika is $\frac{4}{3}$ of the height of Lily, and Sadaf is $\frac{5}{4}$ of the height of Anika, how tall is Sadaf?
(A) $180 \mathrm{~cm}$
(B) $70 \mathrm{~cm}$
(C) $96 \mathrm{~cm}$
(D) $120 \mathrm{~cm}$
(E) $150 \mathrm{~cm}$
Solution 1

Since Lily is $90 \mathrm{~cm}$ tall, Anika is $\frac{4}{3}$ as tall as Lily, and Sadaf is $\frac{5}{4}$ as tall as Anika, then Sadaf is $\frac{5}{4} \times \frac{4}{3} \times 90=\frac{5}{3} \times 90=\frac{450}{3}=150 \mathrm{~cm}$ tall.

## Solution 2

Since Lily is $90 \mathrm{~cm}$ tall and Anika is $\frac{4}{3}$ of her height, then Anika is $\frac{4}{3} \times 90=\frac{360}{3}=120 \mathrm{~cm}$ tall. Since Anika is $120 \mathrm{~cm}$ tall and Sadaf is $\frac{5}{4}$ of her height, then Sadaf is $\frac{5}{4} \times 120=\frac{600}{4}=150 \mathrm{~cm}$ tall.

ANswer: (E)

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