Question

45) A workman is paid 150 for each day he works and is fined 50 for each day
month of 30 days he earned 2100. For how many days did he remain absent​

Answer 1

$\bold{\underline{\underline{\red{Method \:1.}}}}$

Given :

A workman is paid 150 for each day he works and is fined 50 for each day month of 30 days he earned 2100.

Find :

Number of days he remain absent.

Assume :

Let the -

• Number of days in which he absent be "M" days.

Solution :

Total number of days = 30

Present days = 30 - M

For working each day, workman get Rs. 150 and fined Rs. 50 for each day month of 30 days, he earn Rs. 2100.

According to question,

⇒ 150(30 - M) - 50M = 2100

⇒ 4500 - 150M - 50M = 2100

⇒ 4500 - 200M = 2100

⇒ 200M = 4500 - 2100

⇒ 200M = 2400

⇒ 2M = 24

⇒ M = 12

∴ The man remain absent for 12 days.

$\bold{\underline{\underline{\red{Method \:2.}}}}$

Let present days be "N" and absent days be M" days.

According to question,

⇒ 150N - 50M = 2100

⇒ 3N - M = 42

⇒ - M = 42 - 3N

⇒ M = 3N - 42 ____ (eq 1)

Similarly,

⇒ N + M = 30

⇒ N + 3N - 42 = 30 [From (eq 1)]

⇒ 4N = 30 + 42

⇒ 4N = 72

⇒ N = 18

Substitute value of N in (eq 1)

⇒ M = 3(18) - 42

⇒ M = 54 - 42

⇒ M = 12

∴ The man remain absent for 12 days.

Answer 2

$\huge{\pink{\green {\sf\boxed{ANSWER = 12 \:days}}}}$

$\huge{\pink {\sf\underline{Step\: by\: step\: explanation}}}$

Let the number of days he is absent x be

Then, the number of days he is present is 30-x

For the days he is present, he earns 150rs per day

So, he earns 150×(30-x)

For the days he is absent, he is fined 50rs per day

Then, he had to pay a fine of 50 × X

So the money remaining with him at the end of the month is 150×(30-x) -50 × X

and it is given as 2100

So equating,

⟹ 4500-150x-50x=2100

⟹ 2400=20x

implies x is 12.

$\bf{So,\: he\: is\: absent\: for\: 12\: days}$