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

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## Solution

To solve this problem, let’s denote:

Given:

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.