Arun Sharma Solutions for Exercise 1: Review Test

The average marks of a student in ten papers are $80$. If the highest and the lowest score are not considered, the average is $81$. If his highest score is $92$, find the lowest.

A shipping clerk has five boxes of different but unknown weights, each weighing less than $100 \mathrm{kg}$. The clerk weighs the boxes in pairs. The weights obtained are $110, 112, 113, 114, 115, 116, 117, 118, 120$ and $121 \mathrm{kg}$. What is the weight of the heaviest box?

The total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is $₹700$ when there are $25$ boarders and $₹600$ when there are $50$ boarders. What is the average expense per boarder when there are $100$ boarders?

A yearly payment to a servant is $₹90$ plus one turban. The servant leaves the job after nine months and receives $₹65$ and a turban, then find the price of the turban,

A leather factory produces two kinds of bags, standard and deluxe. The profit margin is $₹20$ on a standard bag and $₹30$ on a deluxe bag. Every bag must be processed on machine A and on machine B. The processing times per bag on the two machines are as follows:

The total time available on machine A is $700 \mathrm{hours}$ and on machine B is $1250 \mathrm{hours}$. Among the following production plans, which one meets the machine availability constraints and maximises the profit?

Three math classes: X, Y and Z take an algebra test. The average score of class X is $83$, that of class Y is $76$ and that of class Z is $85$. What is the average score of classes X, Y and Z?

Prabhat ordered four Arrow shirts and some additional Park Avenue shirts. The price of one Arrow shirt was twice that of one Park Avenue shirt. When the order was executed, it was found that the number of the two brands had been interchanged. This increased the bill by $40\%$. The ratio of the number of Arrow shirts to the number of Park Avenue shirts in the original order was _____.

Three group of companies: Tata, Birla and Reliance, announced their average of the annual profit for all years since their establishment. The average profit of Tata is $₹75000 \mathrm{lakhs}$, the average profit of Birla is $₹64000 \mathrm{lakhs}$ and the average profit of Reliance is $₹73000 \mathrm{lakhs}$. The average profit of all years of Tata and Birla together is $₹70000 \mathrm{lakhs}$ and that of Birla and Reliance together is $₹69000 \mathrm{lakhs}$. Approximately, what is the average profit for all the three group of companies?