A labourer is engaged for 20 days on the condition that he will receive ₹ 280 for each day he works and will be fined ₹ 60 for each day he is absent. If he receives ₹ 2540 in all, for how many days did he remain absent?

Let the number of days the labourer was absent be x.

Then, the number of days he worked = (20 - x).

Amount earned for working = 280 x (20 - x) = 5600 - 280x

Amount fined for being absent = 60 × x = 60x

Total amount received = Earnings - Fines

∴ (5600 - 280x) - 60x = 2540

⇒ 5600 - 280x - 60x = 2540 $\quad$ [Removing brackets]

⇒ 5600 - 340x = 2540

⇒ 5600 - 2540 = 340x $\quad$ [Transposing -340x to RHS and +2540 to LHS]

⇒ 3060 = 340x

⇒ x = $\dfrac{3060}{340}$

⇒ x = 9

Hence, the labourer remained absent for 9 days.