Luke had to solve some Chinese 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 3 : 5. At the end of the second week, Luke solved another 30 questions and the number of unsolved questions became ¹₄ of the total number of questions. How many questions did Luke need to solve on the third week to complete his assignment?

	Solved	Unsolved	Total
First week	3x1 = 3 u	5x1 = 5 u	8x1 = 8 u
Second week	+ 30	- 30
Third week	3x2 = 6 u	1x2 = 2 u	4x2 = 8 u

Total number of questions remains same.
LCM of 4 and 8 = 8

Number of questions that Luke solved at the end of the second week
= 6 u - 3 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Number of questions that Luke needed to complete on the third week
= 2 u
= 2 x 10
= 20

Answer(s): 20