(ix) A man gets Rs. 100 per day if he works, but he is fined by Rs 10 per day if he is absent. In the whole month of April he received Rs 1900 only. How many days did he work?

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Solution

$Suppose, the man works for x d a y s and he was absent for y days . Money he gets for x days = Rs 100 x Money he would be fined for y days = Rs 10 y Therefore, he would get = Rs (100 x - 10 y) According to the question, 100 x - 10 y = 1900 \Rightarrow 10 x - y = 190 . . . (1) Days in A pril = 30 Therefore, x + y = 30 \Rightarrow x = 30 - y . . . . (2) Substituting eq (2) in eq (1), 10 \times (30 - y) - y = 190 \Rightarrow 300 - 10 y - y = 190 \Rightarrow 11 y = 110 \Rightarrow y = 10 Substituting y = 10 in eq (2), x = 30 - 10 \Rightarrow x = 20 Therefore, the man works for 20 days .$

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