# Maths | Heuristic | Guess and Check

1. There is a cycle race among 12 kids. A few kids have bi-cycle and others tri-cycle. If there are 29 wheels, then how many are tri-cycle?
2. Ram's age plus the cube of Shyam's age is 1739. Shyam's age plus the cube of Ram's age is 1343. How old are Ram and Shyam?
3. A restaurant has a total of 60 tables. Some of the tables can seat 4 people and some can seat 2 people. All of the seats are occupied when there are 160 people seated. How many tables for 4 are there?
4. In the three equations below, each of the shape represents a number. What is the numerical value of square? \begin{align} &\square+\bigcirc+\triangle=24\\ &\square+\square+\bigcirc=20\\ &\square+\bigcirc+\triangle+\triangle=34 \end{align}
5. A train leaves city A at an average speed of 50 km/hr and heads for city B. Another train leaves city B at an average speed of 40 km/hr and heads for city A. If the route is 360 km long, how many hours will it take for the two trains to meet?
6. Raju gets an interesting job. His pay is increased by Rs 3 every day. He gets a total payment of Rs 125 in five days. How much money he earn on the first day?
7. Solve for the variables $x,y,z,u,v$ and $w$ in the equations below, using the digits from 0 through 5. Every digit should be used only once. \begin{align} x+x+x=x^2 \\ y+z=y \\ uv=u \\ x-v=y\\ y^2=u \\ u+v=w \end{align}
8. Viraj has a few lemons for sale. He sold half of the lemons plus half of a lemon to the first customer. He sold half of the remaining lemons plus half of a lemon to the second customer. He sold half of the remaining lemons and a half of the lemon to the third customer. He sold all lemons without cutting any. How may lemons Viraj initially had?