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Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target?
Verified Answer
Arsh take up a job where in each working day he is given a target for ...
To solve this problem, we can set up the following equation:
105x - 18(30 - x) = 2988
Where x is the number of days that Arsh meets the target.
We can then solve for x by rearranging the terms and solving for x:
105x - 540 + 18x = 2988
123x = 3528
x = 28.8
Since x represents the number of days that Arsh meets the target, and this number must be an integer, we can round down to the nearest whole number to find that Arsh meets the target on 28 days.
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Most Upvoted Answer
Arsh take up a job where in each working day he is given a target for ...
Given:
- Each day, Arsh is given a target.
- If he meets the target, he is paid 105 rupees.
- If he does not meet the target, he is paid 18 rupees less than the previous day.
To find:
- How many days does Arsh meet the target if he is paid a total of 2988 rupees at the end of the month.
Approach:
- Let's assume that Arsh meets the target for 'x' number of days in the month.
- We can calculate the total amount he earns by meeting the target as 105 * x.
- Now, let's calculate the total amount he earns for the remaining days when he does not meet the target.
- For the days when he does not meet the target, he is paid 18 rupees less than the previous day. So, the amount he earns for the first day is 105 - 18 = 87 rupees.
- For the second day, he earns 87 - 18 = 69 rupees, and so on.
- We can calculate the total amount he earns for the days when he does not meet the target as the sum of an arithmetic progression.
- Finally, we can add the two amounts to get the total amount he earns in the month and solve the equation to find the value of 'x'.
Calculation:
Let's assume Arsh meets the target for 'x' number of days in the month.
Amount earned for meeting the target = 105 * x
Amount earned for not meeting the target:
- First day = 105 - 18 = 87 rupees
- Second day = 87 - 18 = 69 rupees
- Third day = 69 - 18 = 51 rupees
- Fourth day = 51 - 18 = 33 rupees
- Fifth day = 33 - 18 = 15 rupees
The pattern continues with a difference of 18 rupees each day.
Amount earned for not meeting the target = Sum of an arithmetic progression with the first term as 87, common difference as -18, and the number of terms as (30 - x) [30 days in a month]
Sum of an arithmetic progression = (n/2) * [2a + (n - 1)d]
= ((30 - x)/2) * [2 * 87 + ((30 - x) - 1) * -18]
= ((30 - x)/2) * [174 - 18(30 - x - 1)]
= ((30 - x)/2) * (174 - 18(31 - x))
= ((30 - x)/2) * (174 - 558 + 18x)
= ((30 - x)/2) * (174 + 18x - 558)
= ((30 - x)/2) * (-384 + 18x)
Total amount earned = Amount earned for meeting the target + Amount earned for not meeting the target
2988 = 105x + ((30 - x)/2) * (-384 + 18x)
Now, we can solve this equation to find the value of 'x' using algebraic methods or by substituting values.
On solving the equation, we find that x = 22.
Therefore, Arsh meets the target for
- Each day, Arsh is given a target.
- If he meets the target, he is paid 105 rupees.
- If he does not meet the target, he is paid 18 rupees less than the previous day.
To find:
- How many days does Arsh meet the target if he is paid a total of 2988 rupees at the end of the month.
Approach:
- Let's assume that Arsh meets the target for 'x' number of days in the month.
- We can calculate the total amount he earns by meeting the target as 105 * x.
- Now, let's calculate the total amount he earns for the remaining days when he does not meet the target.
- For the days when he does not meet the target, he is paid 18 rupees less than the previous day. So, the amount he earns for the first day is 105 - 18 = 87 rupees.
- For the second day, he earns 87 - 18 = 69 rupees, and so on.
- We can calculate the total amount he earns for the days when he does not meet the target as the sum of an arithmetic progression.
- Finally, we can add the two amounts to get the total amount he earns in the month and solve the equation to find the value of 'x'.
Calculation:
Let's assume Arsh meets the target for 'x' number of days in the month.
Amount earned for meeting the target = 105 * x
Amount earned for not meeting the target:
- First day = 105 - 18 = 87 rupees
- Second day = 87 - 18 = 69 rupees
- Third day = 69 - 18 = 51 rupees
- Fourth day = 51 - 18 = 33 rupees
- Fifth day = 33 - 18 = 15 rupees
The pattern continues with a difference of 18 rupees each day.
Amount earned for not meeting the target = Sum of an arithmetic progression with the first term as 87, common difference as -18, and the number of terms as (30 - x) [30 days in a month]
Sum of an arithmetic progression = (n/2) * [2a + (n - 1)d]
= ((30 - x)/2) * [2 * 87 + ((30 - x) - 1) * -18]
= ((30 - x)/2) * [174 - 18(30 - x - 1)]
= ((30 - x)/2) * (174 - 18(31 - x))
= ((30 - x)/2) * (174 - 558 + 18x)
= ((30 - x)/2) * (174 + 18x - 558)
= ((30 - x)/2) * (-384 + 18x)
Total amount earned = Amount earned for meeting the target + Amount earned for not meeting the target
2988 = 105x + ((30 - x)/2) * (-384 + 18x)
Now, we can solve this equation to find the value of 'x' using algebraic methods or by substituting values.
On solving the equation, we find that x = 22.
Therefore, Arsh meets the target for
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Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target?
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Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target?.
Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Arsh take up a job where in each working day he is given a target for each day he meets the target is paid rupees 105 and for each day does not meet the target he paid 18 rupees less. if by the end of the month he paid rupees total 2988 then how many days does he meets the target?.
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