Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar ta

Question

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

Examoogle · Accepted Answer

The correct answer is Option B: 8 hours 15 minutes. Calculate individual work-per-hour rates first ($32/6 = 16/3$ and $40/5 = 8$). Sum them to get the combined rate ($16/3 + 24/3 = 40/3$) and divide the total assignment by this rate.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate individual work-per-hour rates first ($32/6 = 16/3$ and $40/5 = 8$). Sum them to get the combined rate ($16/3 + 24/3 = 40/3$) and divide the total assignment by this rate.

Formula Used: $$Rate = \frac{Work}{Time}$$, $$Total Time = \frac{Total Work}{Combined Rate}$$

Given: Ravi types 32 pages in 6 hours; Kumar types 40 pages in 5 hours; Total pages to type = 110.

Steps: Calculate individual rates: Ravi's rate $R_r = \frac{32}{6} = \frac{16}{3}$ pages/hour. Kumar's rate $R_k = \frac{40}{5} = 8$ pages/hour.. Calculate combined rate: Adding their individual rates gives the combined typing speed: $R_{total} = \frac{16}{3} + 8 = \frac{16+24}{3} = \frac{40}{3}$ pages/hour.. Calculate total time: To find the time for 110 pages, divide total pages by the combined rate: $Time = \frac{110}{40/3} = 110 	imes \frac{3}{40} = \frac{330}{40} = 8.25$ hours.. Convert decimal to time format: 0.25 hours is equal to $0.25 	imes 60 = 15$ minutes. Thus, the total time is 8 hours 15 minutes.

Answer: B is correct because the total combined rate of $\frac{40}{3}$ pages per hour applied to 110 pages results in exactly 8.25 hours, which is 8 hours and 15 minutes.

Exam Tip: This concept is identical to Pipe and Cistern problems where rates of filling tanks are additive. Always work with unit rates per hour to simplify complex fractions.

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