A compositor takes 1 hour 45 minutes to compose 24 pages of a book. How long will he take to compose 64 pages?

First, convert time into minutes:

1 hour = 60 minutes

∴ 1 hour 45 minutes = 60 + 45 = 105 minutes.

Time taken to compose 24 pages = 105 minutes.

Time taken to compose 1 page = $\Big( \dfrac{105}{24}\Big) \text{ minutes} \quad \text{[Less pages, Less time]}$

Time taken to compose 64 pages = $\Big(\dfrac{105}{24} \times 64\Big) \text{ minutes} \quad \text{[More pages, More time]}$

= $\Big(\dfrac{105}{3} \times 8\Big) \text{ minutes} \quad \text{(Dividing 24 and 64 by 8)}$

= 35 x 8 minutes

= 280 minutes (or 4 hours 40 minutes)

Hence, he will take 4 hours 40 minutes to compose 64 pages.