Question

A man was allotted a work for 30 days on the condition that he would get ₹ 10 per day as wage if he reports for work and if he remains absent he would have to pay ₹ 2 as penalty for the day. Ultimately he got ₹ 216. For how many days he remained absent ?

• A. 9
• B. 7
• C. 12
• D. 11

Answer 1

The Correct Option is B

To solve this problem, let's define the variables: Let \( d \) be the number of days the man works, and \( a \) be the number of days he is absent. We know that he was allotted work for 30 days, hence \( d + a = 30 \). He earns ₹ 10 for each day he works, and he pays a penalty of ₹ 2 for each day he is absent. Ultimately, he earned ₹ 216. Therefore, the income equation is:

\((10 \times d) - (2 \times a) = 216\)

Now we have the system of equations:

• 1. \( d + a = 30 \)
• 2. \( 10d - 2a = 216 \)

Substituting \( d = 30 - a \) from the first equation into the second equation:

\(10(30 - a) - 2a = 216\)

\(300 - 10a - 2a = 216\)

\(300 - 12a = 216\)

Simplifying, we get:

\(12a = 300 - 216\)

\(12a = 84\)

\(a = \frac{84}{12}\)

\(a = 7\)

Therefore, he remained absent for 7 days.

The correct answer is 7.