Question

A worker is engaged for $100$ days, on the condition that he will be paid for Rs.$x$ per day for each day he works and will be charged Rs. $y$ per day for each day he is absent. Frame a formula to find his earning $'E'$ in rupees, if he works for $d$ days only
A) $dx - (100 - dy)$
B) $dx - 100y$
C) $dx - (100 - d)y$
D) $dx + (100 - d)y$

Answer 1

Hint:Evaluate the total amount earned by him when he is present and the amount charged on him when he is absent.
To evaluate the formula for total earning subtract the amount charged on him when he is absent from the amount earned by him when he is present.

Complete step-by-step answer:
We are given that a worker is engaged for $100$ days on some conditions.
We’ll discuss our conditions one by one.
Condition - $1$
He will be paid for Rs.$x$ per day when he is present.
We know that he works for $d$ days.
Evaluate the total amount earned by him when he is present.
The total amount earned by him will be the product of the total number of days he is present and earning per day.
Therefore, earning in this case will be $dx$
Condition - $2$
He will be charged Rs.$y$ per day when he is absent.
Total number of days he is engaged is $100$ and he is present for $d$ days, therefore number of days he is absent will be$100 - d$
Evaluate the total amount charged on him when he is absent.
The total amount charged on him will be the product of the number of days he is absent and charged for per day.
Therefore, charges in this case will be $(100 - d)y$
For the formula for total earning $'E'$, Subtract the amount charged on him when he is absent from the amount earned by him when he is present.
Therefore, $E = dx - (100 - d)y$
Hence, option (C) is correct.

Note:
The total earning of any person can be defined as:
Earning = Total amount earned by him by any means - The amount he loses or charged