Question

The average weight of 100 students is 32 kg. The average weight of first 49 students is 30 kg and of last 50 students is 34 kg. What is the weight (in kg) of the 50th student?

A) 25 B) 30 C) 32 D) 33

Answer 1

Given :-

Average weight of 100 students is 32 kg

Average weight of first 49 students is 30 kg

Average weight of last 50 students is 34 kg

Required to find :-

• Weight of the 50th student ?

Formula used :-

$\dagger{\boxed{\rm{Sum \ of \ the \ observations = Mean \times No. \ of \ observations }}}$

Solution :-

Given information :-

• Average weight of 100 students is 32 kg

• Average weight of first 49 students is 30 kg

• Average weight of last 50 students is 34 kg

we need to find the weight of the 50th student

So,

Consider the 1st statement ;

Average weight of 100 students is 32 kg

Here,

we need to find the sum of the weights of 100 students

So,

Using the formula ;

$\dagger{\boxed{\rm{Sum \ of \ the \ observations = Mean \times No. \ of \ observations }}}$

Here,

• Mean = 32

• No. of observations = 100

By solving we get ;

Sum of the observations = 32 x 100

Sum of the observations = 3, 200

>> Sum of the weights of 100 students = 3, 200

Similarly,

Consider the 2nd statement ;

Average weight of first 49 students is 30 kg

we need to find the sum of weights of first 49 students

Here;

• Mean = 30

• No. of observations = 49

Using the above formula ;

Sum of the observations = 30 x 49

Sum of the observations = 1, 470

>> Sum of the weights of first 49 students = 1, 470

However,

Consider the 3rd statement ;

Average weight of last 50 students is 34 kg

we need to find the sum of the weights of last 50 students

here,

• Mean = 34

• No. of observations = 50

Using the above formula ;

Sum of the observations = 34 x 50

Sum of the observations = 1, 700

>> Sum of the weights of last 50 students = 1,700

Now,

We need to find the weight of 50th students

So,

Here we need to use a bit of logic

Subtract the sum of the weights of 100 students with Sum of the first 49 students and last 50 students

Sum of the first 49 students and last 50 students

=> 1470 + 1700

=> 3, 170

According to problem

3200 - 3170

=> 30

This is the weight of the 50th students because the no. of observations in the sum of the first 40 and last 50 students = 99

This is because the weight of 50th students isn't included

So,

Since he was not included the above value which we got by subtracting is the weight of the 50th student

Therefore,

Weight of the 50th student = 30 kg

Conclusion :-

Option - B is correct ✅

Answer 2

$\sf{\huge{\bold{\pink{\bigstar{\boxed{\boxed{Question}}}}}}}$

• The average weight of 100 students is 32 kg. The average weight of first 49 students is 30 kg and of last 50 students is 34 kg. What is the weight (in kg) of the 50th student?

$\sf{\huge{\bold{\pink{\bigstar{\boxed{\boxed{Solution}}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• The average weight of 100 students = 32 kg
• The average weight of first 49 students = 30kg
• The average weight of last 50 students = 34kg

$\sf{\bold{\blue{\underline{\underline{To\:find}}}}}$

• Weight of 50th student = ??

$\sf{\bold{\purple{\underline{\underline{Explanation}}}}}$

$\sf{\bold{\red{\boxed{average = \dfrac{Total\:weight}{no.\:of\:students} }}}}$

For first 49 students :-

$\sf {30 = \dfrac{total\:weight}{49}}$

$\sf{30\times 49 = Total\:weight}$

$\sf{Total\:weight\:of \:first\:49 \:students = 1470kg}$

For last 50 students :-

$\sf {34 = \dfrac{total\:weight}{50}}$

$\sf{34\times 50 = Total\:weight}$

$\sf{Total\:weight\:of \:last\:50 \:students = 1700kg}$

For all 100 students :-

$\sf {32 = \dfrac{total\:weight}{100}}$

$\sf{32\times 100 = Total\:weight}$

$\sf{Total\:weight\:of \:all\:100 \:students = 3200kg}$

Weight of 50th student

Total weight = weight of first 49 students + weight of last 50 students + weight of 50th student

3200 = 1470 + 1700 + weight of 50th student

3200 = 3170 + weight of 50th student

weight of 50th student = (3200 - 3170 )kg

weight of 50th student = 30kg

$\sf{\bold{\orange{\boxed{weight\:of\:50th\:student = \:30kg = \:optionB}}}}$

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