Jaya baked mufins using paper liners and cherries. Some paper liner packets contain $8$ liners, while others contain $10$ liners. A packet of cherry contains $6$ cherries. Every mufin Jaya baked contained $1$ cherry. All cherries and paper liners were used up.

What can be the minimum number of mufins baked by her?

Jaya baked and sold vanilla mufins at $₹15$ and chocolate mufin at $₹18$. She earned equal amounts from the sale of both mufins. 

How many vanilla and chocolate mufins did she sell?

Three numbers are in the ratio $1:2:3$ and their $\mathrm{HCF}$is $6$, the numbers are

The measurement of a rectangular piece of land is to be verified quickly while minimising the errors in the measurement. The land has a length of $96 \mathrm{ft}$ and a width of $56 \mathrm{ft}$. 

What is the length of the longest measuring stick that can be used to measure each side of the land, without breaking it?

The number of students studying in the grades $5$ and $6$ are $120$ and $160$ respectively. For a specific annual fest of the school, the students of the grades $5, 6,$ and $7$ were combined and made into groups. The maximum number of students they could form per group was $5$, to maintain equal members in every group, without leaving out any student.

Which of the following could be the number of students studying in grade $7$?

Malini has a number which is divisible by both $8$ and $12$.

Which of the following is the least number that definitely divides Malini's number without leaving a remainder?

Two friends, $A$ and $B$, each of them thought of a number. The only common factor of the two numbers other than $1$ is $3.$ The product of the numbers is $180$.

Which of the following is their LCM?