A labourer is engaged for 20 days on the condition that he will receive Rs.120 for each day, he works and will be fined Rs.10 for each day he is absent. If he receives Rs.1880 in all, for how many days did he remain absent?

Let's denote the number of days the laborer worked as "D" and the number of days he remained absent as "A."

According to the given information:

He receives Rs. 120 for each day he works.
He will be fined Rs. 10 for each day he is absent.
So, his total earnings for the days he worked would be 120D, and his total fine for the days he remained absent would be 10A.

It's also mentioned that he received a total of Rs. 1880 in all, so we can write the equation:

Total earnings - Total fine = Rs. 1880

120D - 10A = 1880

Now, let's work with the information that the laborer was engaged for 20 days. This means that the total number of days (D + A) is 20:

D + A = 20

We can now use these two equations as a system of linear equations to solve for D and A. First, let's solve the second equation for D:

D = 20 - A

Now, substitute this expression for D into the first equation:

120(20 - A) - 10A = 1880

Now, distribute the 120 on the left side of the equation:

2400 - 120A - 10A = 1880

Combine like terms:

2400 - 130A = 1880

Now, subtract 2400 from both sides of the equation:

-130A = 1880 - 2400

-130A = -520

Finally, divide both sides by -130 to solve for A:

A = -520 / -130
A = 4

So, the laborer remained absent for 4 days.