Working Together, John and Jack can Type 20 Pages in One Hour GMAT Problem Solving

Question: Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour provided Jack increased his typing speed by 25%, what is the ratio of Jack’s normal typing speed to that of John?

1. \(\frac{1}{3}\)
2. \(\frac{2}{5}\)
3. \(\frac{1}{2}\)
4. \(\frac{2}{3}\)
5. \(\frac{3}{5}\)

“Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour provided Jack increased his typing speed by 25%, what is the ratio of Jack’s normal typing speed to that of John?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

There is only one solution to this problem.

Let the rate of John be x pages per hour and the rate of Jack y pages per hour. Then as we can sum the rates and rate * time = job then (x+y) * 1 = 20
So, we have that x + y = 20;
They would be able to type 22 pages in one hour provided Jack increased his typing speed by 25%: (x + 1.25y) * 1 – 22.
So, we also have that x + 1.25y = 22;

Question: \(\frac{y}{x}=?\)

Subtract (1) from (2): x + 1.25y – (x + y) = 22 – 20, which gives y = 8, so x = 12.

Therefore, \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\)

OR

If by increasing the rate of Jack by 25%, 2 more pages can be types in one hour, then we can directly write: 0.25 y = 2 which gives y = 8 and x = 12

Therefore, \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\)

Correct Answer: D

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