Question 24

A three-digit number 2a3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9. The value of $$(b - a)$$ is

Solution

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For 5b9 to be divisible by 9, $$5 + b + 9 = 14 + b$$ must be a multiple of 9, so $$b = 4$$. Then $$2a3 = 549 - 326 = 223$$, giving $$a = 2$$. So $$b - a = 4 - 2 = 2$$.

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