On January 1st, 2023, a person saved ₹1. On January 2nd, 2023, he saved ₹2 more than the previous day, and so on. At the end of which date was his total savings a perfect square as well as a perfect cube?

A person allows a 10% discount on the marked price of a toy for cash payment and still makes a profit of 10%. What is the cost price of the toy whose marked price is Rs. 770?

A circular target (plate) of diameter 1 metre in archery is painted with four colours from inside to outside — red, blue, yellow and white. The radius of the red band is 0.20 metre. The widths of the remaining bands are equal. When arrows are shot at this circular target, what is the probability that the arrows hit the red part of the target?

In a race, a competitor has to collect 6 apples which are kept in a straight line on a track and a bucket is placed at the beginning of the track which is the starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run (the first apple being at a distance of 5 metres from the bucket and the rest of the apples being 3 metres apart)?

In a family of five persons, the average income per person is Rs. 10,000 per month. What will be the average income per person per month in the same family if the income of one of the persons increases by Rs. 1,20,000 per year?

W completes 25% of a piece of work in 30 days, X completes 1/4 of the work in 10 days, Y completes 40% of the work in 40 days and Z completes 1/3 of the work in 13 days. Who will complete the work first?

A and B walk around a circular park. They start at 8:00 am from the same point in opposite directions. A and B walk at the rate of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 8:00 am and before 9:30 am?