An employer pays ₹20 for each day a works, and forfeits ₹ 3 for each day he is idle. At the end of 60 days, a worker gets ₹280. For how many days did the worker remain idle? (a) 28 (b) 40 (c) 52 (d) 60

Solution

To solve this problem, let’s denote:

• \(x\) as the number of days the worker worked.
• \(y\) as the number of days the worker remained idle.

Given:

• The worker is paid ₹20 for each day worked.
• The worker forfeits ₹3 for each day idle.
• The total number of days is 60, so \(x + y = 60\).
• The total amount paid to the worker is ₹280.

The total amount earned for working \(x\) days and the amount forfeited for \(y\) idle days can be represented as:

\[
20x – 3y = 280
\]

Since \(x + y = 60\), we can express \(y\) in terms of \(x\):

\[
y = 60 – x
\]

Substituting \(y\) in the equation for the total amount gives us:

\[
20x – 3(60 – x) = 280
\]

Simplifying this equation to find \(x\):

\[
20x – 180 + 3x = 280
\]

\[
23x = 460
\]

\[
x = 20
\]

Since \(x + y = 60\), and we now know \(x = 20\), we can find \(y\):

\[
20 + y = 60
\]

\[
y = 40
\]

Therefore, the worker remained idle for 40 days.

The correct answer is (b) 40.