Question

The average age of 15 students is 11 years and 3 month which increased by one year and one and half months when the age of teacher is included the teacher in years and months​

Answer 1

Gɪᴠᴇɴ :-

• The average age of 15 students is 11 years and 3 month .
• If Teacher age is added than , average increased by one year and one and half months .

Tᴏ Fɪɴᴅ :-

• Age of Teacher in Years and months.

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• Average = (sum of Observation) / (Total Number of Observation).
• 1 Year = 12 Months

Sᴏʟᴜᴛɪᴏɴ :-

→ Average age of 15 Students = 11 years + 3 months = 11 * 12 + 3 = 135 Months.

→ Total age of 15 Students = 15 * 135 = 2025 Months. ------ Equation (1).

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Now,

→ when Teacher is added , Total Members in class = 15 students + 1 Teacher = 15 + 1 = 16

→ New Average = 11 years + 3 months + 1 year + 1.5 months . = 12 Years + 4.5 Months = 12 * 12 + 4.5 = 144 + 4.5 = 148.5 Months.

So,

→ Total age of 16 Members of class = 16 * 148.5 = 2376 months ---------- Equation (2).

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Therefore ,

→ Teacher Age = Equation (2) - Equation (1)

→ Teacher Age = 2376 - 2025

→ Teacher Age = 351 Months .

→ Teacher Age = (351/12) Years.

→ Teacher Age = 29 Years + 3 Months (Ans.)

Hence, Age of Teacher is 29 Years & 3 Months.

Answer 2

Aɴꜱᴡᴇʀ

➜ Age of the teacher is 29 years and 3 months

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Gɪᴠᴇɴ

➤ The average age of 15 students is 11 years 3 months

➤ If the age of the teacher was added then the average age gets added by one year ½ months

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ᴛᴏ ꜰɪɴᴅ

✭ The age of the teachers in years and months

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Sᴛᴇᴘꜱ

❍ So if the average age of 15 students is 11 years and 3 months ,then it can also be written as,

$\large \tt \longrightarrow11 \times 12 + 3 = 135 \: months$

So then as thee are 15 students,their age will be

$\large \tt \longrightarrow{}15 \times 135 = \red{2025 \: months}......(1)$

➠ In case 2 the teacher gets added so then there will be a total of 16 students that is 15+1.

❍ So then the new average age is given by,

$\large \tt \mapsto{}11 + 1 + 3 + 1.5 = {12 \: years \: 4.5 \: months} \\ \\ \large \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (or) \\ \\ \large \tt \mapsto12 \times 12 + 4.5 = {148.5 \: months}$

And again there are 16 members in the class so a total of,

$\large \tt \mapsto{}16 \times 148.5 = \red{2376 \: months}.......2$

❍ Finally to find the age of the teacher we have to subtract Equation 1 from Equation 2.

$\large \tt{} \dashrightarrow2376 - 2025 = 351$

✴ But here it is in months but the given data is in years and months so let's convert our final answer too,

$\large \tt \dashrightarrow{} \cancel\frac{351}{12} \\ \\ \large \tt \pink{ \dashrightarrow{}29.25}$

✪ So the age of the teacher is 29 years and 3 months.

Note :-

✏ We made .25 as 3 months because 25% of 12 monthes is 3 months.

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