The average age of the students in a class of 50 is 13. The weight of each student is directly proportional to the height. A 165 cm tall student has a weight of 33 kg. The average weight of the class is:a)33 kgb)39 kgc)36 kgd)Data insufficientCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

How did you come to know that the weight of 33 kg is of 11 years old student?

Answer

Since the weight is directly proportional to height and height is directly proportional to age, we can say weight is directly proportional to age. The average age is 13.
Since 11 year old weighs 33 kg, 13 year old would weigh = 33*(13/11) =39 kg

Answer

Given information:
- Average age of the students in a class of 50 is 13
- Weight of each student is directly proportional to the height
- A 165 cm tall student has a weight of 33 kg

To find: Average weight of the class

Solution:
Let's first find the weight of the 165 cm tall student per unit height:
Weight per unit height = 33 kg / 165 cm
Weight per unit height = 0.2 kg/cm

Now, we can find the weight of any other student in the class using their height:
Weight = (Height) x (Weight per unit height)

We know that the average age of the students in the class is 13. Let's assume that the heights of the students are also normally distributed around a mean value (which we don't know). In that case, we can use the concept of standard deviation to estimate the average weight of the class:

- First, let's assume that the standard deviation of the heights is 10 cm (this is just an assumption for the sake of calculation).
- Then, we can find the range of heights that covers 68% of the students (since heights are normally distributed, this range will be within 1 standard deviation from the mean):
Mean height = 165 cm
Lower limit of height range = 165 cm - 10 cm = 155 cm
Upper limit of height range = 165 cm + 10 cm = 175 cm
- Now, we can calculate the weight of a student at each end of this height range:
Weight at lower limit = 155 cm x 0.2 kg/cm = 31 kg
Weight at upper limit = 175 cm x 0.2 kg/cm = 35 kg
- Finally, we can find the average weight of the class by taking the mean of these two weights:
Average weight = (31 kg + 35 kg) / 2 = 33 kg

Therefore, the correct answer is option (B) 39 kg.

Similar Quant Doubts

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?

Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?

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