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A daily wager is paid Rs 15 for every day he works and fines Rs 8 for each day he is absent. In October he earned Rs 258. How many days was he absent?
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One can solve the problem by reducing it to a system of two equations or to a single equation.
More elegant way is to use the common sense and mental math.
The solution is = = = 9 days.
What is 15*31 in this formula? - It is the amount the worker had earned if he worked every day of 31 days of October.
But he earned only Rs 258. It is because he was absent on some days in October. It is the same as if he returned Rs 15
for each day he was absent, and returned also Rs 8 as the fines. 15 + 8 = 23, and it is the denominator.
Now, the numerator is exactly the amount he "returned" or loose for his absent days.
At last, the ratio in the formula is exactly the number of days the worker was absent.
The problem is solved.
The answer is: 9 days.