Question

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?
(a) 20 days
(b) 22 days
(c) 29 days
(d) 23 days

Answer 1

- Hint: Let ‘x’ be the number of days he works and ‘y’ be the number of days absent. The sum of (x + y) gives the total number of days in April. He gets Rs.100 on ‘x’ days and loss of Rs.10 on ‘y’ days. Thus frame the equations and solve it to get the values of x and y.

Complete step-by-step solution -
It is said that a man gets Rs.100 per day for every day.
He will be fined Rs.10 per day if he is absent.
In the month of April he gets Rs.1900.
Let us consider ‘x’ as the number of days he worked in April and ‘y’ as the number of days he was absent. We know that in the month of April there are 30 days.
Out of these 30 days, he is present on ‘x’ days and absent on ‘y’ days. Thus we can form a equation as,
\[\Rightarrow x+y=30\] - (1)
According to the question, he gets Rs.100 on ‘x’ days and reduces Rs.10 on ‘y’ days and totally he gets only Rs.1900. Thus we can form the equation as,
\[\Rightarrow 100x-10y=1900\]
Simplifying it we get,
\[\Rightarrow 10x-y=190\] - (2)
Now let us add both equations (1) and (2).

\[x+y=30\]
\[\underline{10x-y=190}\]
\[11x=220\]
\[\therefore x=\dfrac{220}{11}=20\]
Hence the man worked 20 days in April.
\[\therefore \] Option (a) is the correct answer.

Note: If the man worked everything in the month of April he would have got Rs.3000. But he only got Rs.1900. We found that he worked for 20 days.
\[\therefore \] Payment for 20 days = 20 \[\times \] Rs.100 = Rs.2000. The fine is reduced from this. He was absent for 10 days. Thus his fine = 10 \[\times \] Rs.10 = Rs.100.
\[\therefore \] His payment in the month of April = Rs.2000 – Rs.100 = Rs.1900.