Question
For February, the library plans next year to increase
the total issues by 25%, while keeping Science issues the same as this year. The extra issues will be made up only by increasing Arts and Commerce issues equally in absolute numbers (i.e., the number added to Arts is the same as the number added to Commerce). What will be the new Arts issues in February under this plan?Solution
ATQ, From row and column totals: Jan: 120 + A_Jan + 80 = 300 ⇒ A_Jan = 100 Feb: S_Feb + 110 + 70 = 320 ⇒ S_Feb = 140 Mar: 160 + 90 + C_Mar = 350 ⇒ C_Mar = 100 Apr: 100 + A_Apr + 120 = 350 ⇒ A_Apr = 130 So the complete table (for solution/reference) is: 
Current February data: Science = 140 Arts = 110 Commerce= 70 Total = 320 New total issues next year = 25% more than 320 = 1.25 × 320 = 400 Science issues remain = 140 So Arts + Commerce (new) = 400 − 140 = 260 Currently Arts + Commerce = 110 + 70 = 180 Increase needed in (Arts + Commerce) = 260 − 180 = 80 Given the extra is equally split between Arts and Commerce: So each increases by 80 ÷ 2 = 40 New Arts issues in Feb = 110 + 40 = 150
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