Kiran and Harpreet live in the same society. Both of them do not like visiting the busy neighbourhood grocery store for their daily grocery needs. So, they list out their bulk grocery requirements and visit the supermarket at fixed intervals. Kiran goes to the supermarket every $64$ days and Harpreet goes to the same every $72$ days. They met each other one day.

How many days later will they meet each other again?

Ajay always goes to his favourite barber shop every $4^{\mathrm{th}}$ day for styling his beard. Wednesday is a very busy day for Ajay as he has a lot of meetings on Wednesday, so he never wants to go to the barber shop on Wednesday. But this week, due to some urgency, he has to go to the barber shop on Wednesday itself.

If he goes to the barbershop this Wednesday, then how many days later will he be visiting the barber shop again on a Wednesday?

A builder is planning to modernize the rectangular shaped hall whose dimensions are $35 \times 30$ (feet) with square tiles of same size. He wants to buy large tiles as the cost of small tiles is more than large tiles. What are the dimensions of the largest tiles that he can buy(in feet) ?

Non-terminating and repeating decimal are represented by putting a bar on the repeated part. For example: $a.bcbcbcbcbcb.....$ can be represented as $a.\overline{bc}$. 

Angad went to a shop to buy a toffee. When he asked about the price of toffee to the shopkeeper, the shopkeeper told him the cost of the toffee is $₹1.325325. . . .$ , he wants to convert the cost into a fractional form. Help Angad to convert the cost of toffee into a fractional form.

In today’s class, Arjun and Rahul studied Euclid’s Division Lemma and Euclid's division algorithm.

Euclid's division algorithm states that for any two given positive integers $a$ and $b$, there exist unique integers $q$ and $r$ satisfying $a=bq+r, 0\le r<b$.

Arjun asked Rahul to find the H.C.F of $1260$ and $7344$ using Euclid's division algorithm. Rahul found the answer as $36$.

Is Rahul correct? Show the process Rahul used to get the answer.

Raj is playing "Roll a dice-Number game" with his friend Rahul. If he gets a $5$ on the dice, he is supposed to collect an Irrational number from Rahul. Rahul has the set of numbers: $\left\{3, 3.14, \sqrt{2},\frac{1}{2}\right\}$ with him. Raj takes the turn and rolls the dice. He gets a $5$ on the dice, so he picks up the number $\sqrt{2}$ from Rahul. Simran, who was just observing the game, said that the number collected by Raj is not an Irrational number. Help Raj to prove that the number collected by him from Rahul is an Irrational number.

A milk processing company has two different suppliers delivering milk to them. One of them has all their jars of $250$ litres capacity. The other one has jars of capacity $425$ litres. The Operations department of the company now wants to minimise cost, and wants to buy only one size of container which can measure both the jar capacities in complete multiples. What is the maximum capacity of the container that the Operations department should get?

Indian army contingent of $616$ members are to march behind the Indian army band of $32$ members in republic day parade of $2023$ at Raj Path.

The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?