A man is employed for 30 days on the condition that he receives Rs.100 for each day he works and loses Rs.25 for each day he is absent. He gets Rs.2,000 in all. For how many days was he absent?
Question
A man is employed for 30 days on the condition that he receives Rs.100 for each day he works and loses Rs.25 for each day he is absent. He gets Rs.2,000 in all. For how many days was he absent?
Solution
Let's denote the number of days the man worked as 'x' and the number of days he was absent as 'y'.
From the problem, we know that:
- x + y = 30 (since the total number of days is 30)
- 100x - 25y = 2000 (since he earns Rs.100 for each day he works and loses Rs.25 for each day he is absent, and his total earnings are Rs.2000)
We can solve these two equations to find the values of x and y.
First, multiply the first equation by 25 to make the coefficients of y the same in both equations:
25x + 25y = 750
Now, subtract this new equation from the second equation:
100x - 25x = 2000 - 750 75x = 1250
Divide both sides by 75 to find x:
x = 1250 / 75 x = 16.67
Since the number of days worked must be a whole number, we round this up to 17.
Substitute x = 17 into the first equation to find y:
17 + y = 30 y = 30 - 17 y = 13
So, the man was absent for 13 days.
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