Archie had to solve some Science questions during a 3-week school holidays. At the end of the first week, the ratio of the number of questions solved to the number of questions unsolved was 2 : 7. At the end of the second week, Archie solved another 40 questions and the number of unsolved questions became ¹₃ of the total number of questions. How many questions did Archie need to solve on the third week to complete his assignment?

	Solved	Unsolved	Total
First week	2x1 = 2 u	7x1 = 7 u	9x1 = 9 u
Second week	+ 40	- 40
Third week	2x3 = 6 u	1x3 = 3 u	3x3 = 9 u

Total number of questions remains same.
LCM of 3 and 9 = 9

Number of questions that Archie solved at the end of the second week
= 6 u - 2 u
= 4 u

4 u = 40

1 u = 40 ÷ 4 = 10

Number of questions that Archie needed to complete on the third week
= 3 u
= 3 x 10
= 30

Answer(s): 30