NumericalModerate3 marks
If (3a + 2b) : (5a + 3b) = 18 : 29. Find a : b.
Topic: Recurring deposit / interest
Previous-year question practice database
Answer
Solution diagram
Exam answer
Given:
(3a + 2b)/(5a + 3b) = 18/29
Cross-multiplying:
29(3a + 2b) = 18(5a + 3b)
87a + 58b = 90a + 54b
58b − 54b = 90a − 87a
4b = 3a
Therefore:
a/b = 4/3
Answer:
a : b = 4 : 3.
Explanation
Convert the ratio statement into a proportion and cross-multiply. Rearranging the resulting linear equation gives 3a = 4b, hence a : b = 4 : 3.
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