Arun Sharma Solutions for Exercise 2: Level of Difficulty

Find the average weight of four packets, if it is known that the weight of the first packet is $20 \mathrm{kg}$and the weights of the second, third and fourth packets' each is defined by $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2-\frac{2}{5}\times \left({\mathrm{x}}^2\right)$ where $\mathrm{x}=$$10$.

There are five boxes in a box hold. The weight of the first box is $40 \mathrm{kg}$ and the weight of the second box is $50\%$ higher than the weight of the third box, whose weight is $25\%$ higher than the first boxes' weight. The fourth box at $150 \mathrm{kg}$ is $50\%$ heavier than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.

There are five boxes in a box hold. The weight of the first box is $40 \mathrm{kg}$ and the weight of the second box is $50\%$ higher than the weight of the third box, whose weight is $25\%$ higher than the first boxes' weight. The fourth box at $150 \mathrm{kg}$ is $50\%$ heavier than the fifth box. Find the difference in the average weight of the heaviest three and the lightest three.

$20$ persons went to a hotel for a combined dinner party. $15$of them  spent $₹90$ each on their dinner and rest spent $₹30$ more than the average expenditure of all the $20.$ What was  the total money spent  ( in $₹$ ) by them$?$

There were $30$ students in a hostel. Due the admission of$20$ new students, the expenses of the mess increases by $₹1600$  per day while the average expenditure per head diminished by $₹8.$ What was the original expenditure (in $₹$) of the mess$?$

The average weight of $23$ boxes is $3$ kg. If the weight of the container (in which the boxes are kept)is included, the calculated average weight per box increase by $1$kg . What is the weight of container. 

Find $\sum _{r=1}^n(n+1)r$ 

Read the following passage and answer the following question that follows.

Aman, Binod, Charan, Dharam and Ehsaan are the members of the same family. Each and everyone loves one another very much. Their birthdays are in different months and on different dates. Aman remembers that his birthday is between $25th$ and $30th$, of Binod it is between $20th$and $25th$, of Charan it is between $10th$and $20th$, of Dharam it is between $5th$ and $10th$ and of Ehsaan it is between $1st$and $5th$ of the month. The sum of the date of birth is defined as the addition of the date and the month, for example $12th$ January will be written as $12/1$ and will add to a sum of the date of $13$. (Between $25th$and $30th$ includes $25$ and $30$).

If the dates of birth, of four of them are prime numbers, then find the maximum average of the sum of their dates of birth?