Paul had to solve some History 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 : 5. At the end of the second week, Paul solved another 40 questions and the number of unsolved questions became ¹₃ of the total number of questions. How many questions did Paul need to solve on the third week to complete his assignment?

	Solved	Unsolved	Total
First week	2x3 = 6 u	5x3 = 15 u	7x3 = 21 u
Second week	+ 40	- 40
Third week	2x7 = 14 u	1x7 = 7 u	3x7 = 21 u

Total number of questions remains same.
LCM of 3 and 7 = 21

Number of questions that Paul solved at the end of the second week
= 14 u - 6 u
= 8 u

8 u = 40

1 u = 40 ÷ 8 = 5

Number of questions that Paul needed to complete on the third week
= 7 u
= 7 x 5
= 35

Answer(s): 35