There are two batches A and B of a class. Batch A consists of 44 students and batch B consists of 56 students. The average weight (in kg) of the whole class, if the average weight of batch A is 43 kg and that of batch B is 39 kg, is:?

Question

There are two batches A and B of a class. Batch A consists of 44 students and batch B consists of 56 students. The average weight (in kg) of the whole class, if the average weight of batch A is 43 kg and that of batch B is 39 kg, is:?

40.76
42.65
39.68
41.59

LohaHridoy

6 views

2025-01-04 04:42

1 Answers

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

Option 1 : 40.76

Given:
Batch A consists of 44 students and batch B consists of 56 student.

The average weight of batch A is 43 kg and that of batch B is 39 kg.

Formula used:

Combined average of 2 groups = (ma + nb)/(m + n)

Here,

m = numbers of members in group 1

n = numbers of members in group 2

a = average of group 1

b = average of group 2

Calculation:

Let the average of whole class be x.

x = (ma + nb)/(m + n)

⇒ x = (44 × 43 + 56 × 39/(44 + 56)

⇒ x = (1892 + 2184)/100

⇒ x = 4076/100

⇒ x = 40.76

∴ The average weight of whole class is 40.76 kg.

Alternate Method

Let the average weight of the whole class be 40 kg.

the average weight of batch A is exceeded by (43 - 40) = 3 kg

The total weight of batch A is exceeded by (44 × 3) = 132 kg

the average weight of batch B is inferior by (40 - 39) = 1 kg

The total weight of batch B is inferior by (56 × 1) = 56 kg

The total weight of the whole class is exceeded by (132 - 56) = 76 kg

The average of the whole class is exceeded by 76/100 = 0.76 kg

Required average = 40 + 0.76

⇒ Average = 40.76

∴ The average weight of the whole class is 40.76 kg.