Average weight of 12 students is increased by 1 kg when one of the students whose weight is 40 kg replaced by a new student. What is the weight of new student?

Question

Average weight of 12 students is increased by 1 kg when one of the students whose weight is 40 kg replaced by a new student. What is the weight of new student?

49 kg
51 kg
50 kg
52 kg

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 4 : 52 kg

Given:

Total student = 12

Replaced student weight = 40kg

Increment in average = 1kg

Concept:

Average = Total sum/ Total persons

Calculation:

Let average age of 12 students = a

Sum of age of 12 students = 12a

Old student weight = 40

New student weight = N

New average weight = a + 1

∴ (12a — 40 + N)/12 = a + 1

⇒ 12a — 40 + N = 12a + 12

⇒ 12a —40 + N = 12a + 12

⇒ N = 12 + 40

⇒ N = 52

New student weight = 52 kg

Shortcut Trick

Formula used:

Weight of new student = Previous average weight + increase in average weight × number of students.

Calculations:

Weight of the new student = 40 + 1 × 12 = 52 kg