M L Aggarwal Solutions for Chapter: Linear Equations and Inequalities in One Variable, Exercise 4: Higher Order Thinking Skills(HOTS)

A man covers a distance of $24\mathrm{km}$ in $3\frac{1}{2}$ hours partly on foot at the speed of $4.5\mathrm{km}/\mathrm{h}$ and partly on bicycle at the speed of $10\mathrm{km} /\mathrm{h}.$Find the distance covered on foot.

The perimeter of a rectangle is$240\mathrm{cm}$. If its length is decreased by $10\%$ and breadth is increased by $20\%$
we get the same perimeter. Find the original length and breadth of the rectangle.

A person preparing a medicine wants to convert $15\%$ alcohol solution into$32\%$ alcohol solution. Find how
much pure alcohol he should mix in $400 \mathrm{ml}$ of $15\%$ alcohol solution to obtain required solution?

Rahul covers a distance from $P to Q$ on a bicycle at $10 \mathrm{km}/\mathrm{h}$ and returns back at $9\mathrm{km}/\mathrm{h}$. Anuj covers the
distance from$P$ to $\mathrm{Q}$ and $\mathrm{Q}$ to $\mathrm{P}$ both at $12 \mathrm{km} / \mathrm{h}.$ On calculating we find that Anuj took $10 \mathrm{minutes}$ less than
Rahul. Find the distance between $P$ and$Q$

solve

$\frac{x-b-c}{a}+\frac{x-c-a}{b}+\frac{x-a-b}{c}=3$ and find value of $x$.