In order to complete a reading assignment on time, Terry planned to read 90 pages per day.However,she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all Terry have to complete the assignment on time?

A.15
B.16
C.25
D.40
E.46

This is a weighted average/mixture problem.

First set of days: Average number of pages per day = 75.
Last 6 days: Average number of pages per day = 690/6 = 115.
Mixture of the two sets of days: Average number of pages per day = 90.

Let F = the first set of days and L = the last 6 days.
To determine the ratio of F to L in the mixture, use ALLIGATION:

Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the mixture average in the middle.
F 75-----------------90----------------115 L

Step 2: Calculate the distances between the averages.
F 75--------15-------90--------25------115 L

Step 3: Determine the ratio in the mixture.
The required ratio of F to L is the RECIPROCAL of the distances in red.
F:L = 25:15 = 5:3.

Since the actual value of L is 6 days, and F:L = 5:3 = 10:6, F = 10 and L = 6.
Thus, the total number of days = F+L = 10+6 = 16.

The correct answer is B.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?

A) 15

B) 16

C) 25

D) 40

E) 46

An alternate approach is to plug in the answers, which represent the total number of days.
Since the planned rate was 90 pages per day, the total number of pages must be a multiple of 10.
Over the last 6 days, the total number of pages read = 690.
Thus, the total number of pages read at a rate of 75 pages per day must be a multiple of 10.
Answer choice A (15 days) implies 9 days at 75 pages per day.
Answer choice C (25 days) implies 19 days at 75 pages per day.
Neither of these answers will yield a total number of pages that is a multiple of 10.
Eliminate A and C.

Answer choice B: 16 days
10 days at 75 pages per day + 690 pages over the last 6 days = 10*75 + 690 = 1440.
16 days at 90 pages per day = 16*90 = 1440.
Success!

The correct answer is B.

Thank you Mitch.

The explanation is very clear. Thanks

Thank you Mitch.

The explanation is very clear. Thanks