There were $35$ students in a hostel. If the number of students is increased by $7,$ the expenditure on food increase by $Rs. \,42$ per $day$ while the average expenditure of students is reduced by $Rs.\, 1.$ What was the initial expenditure on food per day? (in $Rs.$)

A cricketer scored some runs in his continuous $9$ innings. He scored $100$ runs in his $10^{th}$ innings and this increased his average by $8$ runs. What was the average of his runs at the end of $10^{th}$ innings?

A motorist covered the first $20\, km$ of his journey in 30 mifitutes and the remaining $29\, km$ in $40\, minutes$. His average speed in $km / hr$ is:

A batsman, in his $12^{th}$ innings, makes a score of $63$ runs and thereby increases his average score by $2.$ The average of his score after $12^{th}$ innings is

In a coconut grove, $(x+2)$ trees yield $60$ $nuts$ per $year,$ $x$ trees yield $120\, nuts$ per $ year,$ and $(x-2)$ trees yield $180 \,nuts$ per $year$. If the average yield per $year$ per tree be $100,$ find the value of $x .$