Olympiad/HOTS corner

Mathematics textbook for class $\mathrm{VI}$ has $320$ pages. The chapter ‘symmetry’ runs from page $261$ to page $272.$ The ratio of the number of pages of this chapter to the total number of pages in the book is

$\frac{25\% of 50\% of 100\%}{25 of100 \times 50\%of100}$is equal to ________________

If $a:b=2\frac{1}{2}:1\frac{2}{3}$ and $b:c=1\frac{1}{4}:3\frac{1}{2},$ then find $a:b:c$.

Sushma sells an article at a loss of $12\%$. If she had sold it for $₹ 50.48$ more, then she would have earned a profit of $8\%$. Find the cost price of the article.

The number of students in a school increased by $8⁒$ annually. If there are $71280$ students in the school, then how many students were there last year?

The ages of Ruchi and Suchi are in the ratio $6:1$. The sum of their ages is $56$ years. What is the ratio of their ages after $6$ years?

Raghav was measuring a piece of cloth of length $2.5 \mathrm{m}$ but by mistake he measured its length as $255 \mathrm{cm}$. Find the change in percentage in measuring the length.

Kanita lent $₹ 6400$ to Richa and Renuka each at $15\%$ per annum for $5$ years and $3\frac{1}{2}$ years respectively. Find the difference between the simple interests paid by them.