Select the correct answerP, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours. R can type as many pages as P can during seven hours. How many pages does each of them type per hour?Options15, 17, 2214, 17, 2015, 18, 2116, 18, 22
Question
Select the correct answerP, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours. R can type as many pages as P can during seven hours. How many pages does each of them type per hour?Options15, 17, 2214, 17, 2015, 18, 2116, 18, 22
Solution
Let's denote the number of pages each typist can type per hour as P, Q, and R respectively.
From the problem, we know that:
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P + Q + R = 216/4 = 54 (since together they can type 216 pages in 4 hours)
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R = Q + (Q - P) (since R can type as many pages more than Q as Q can type more than P)
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R * 5 = P * 7 (since R can type as many pages in 5 hours as P can in 7 hours)
We can simplify equation 2) to get R = 2Q - P.
Substitute R from equation 3) into equation 2) to get 2Q - P = P * 7/5.
Solving this equation gives Q = 15 and P = 14.
Substitute P and Q into equation 1) to get R = 54 - 14 - 15 = 25.
So, the number of pages each typist can type per hour is P = 14, Q = 15, and R = 25.
Therefore, the correct answer is not in the options provided.
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