Analytical Mathematics

A chef has three ingredients: flour, sugar, and butter. He needs to prepare a cake with the following conditions:

1. Use exactly twice as much flour as sugar.
2. Use exactly half as much butter as sugar.
3. The total weight of all ingredients should be 600 grams.

How much of each ingredient should he use?

You are given with six numbers – 1, 2, 3, 4, 5 and 6. You can arrange them in any order and you can use all four mathematics expressions i.e. add, subtract, multiply and divide and also parenthesis. The result must be 278.

There are three other rules
1) You can only use a number once.
2) It is not compulsory to use all the six numbers.
3) You can’t join numbers i.e. you can’t use 1, 2 and 3 as 123.

In a pizza parlour, you have to pay a certain amount to add extra toppings. Now the price for toppings is given in a pair below. Can you find out what each topping costs?

Corn & Jalapeno $7
Mushrooms & Extra Cheese $6
Paprika & Tomatoes $2
Onion & Jalapeno $5
Green chilly & Paprika $4
Tomatoes & Onion $3
Extra Cheese & Paprika $5

Please note that the toppings are priced w.r.t. whole dollar increments (no fraction prices).

Pooja gave Neha as many euros as Neha started with.
Neha then gave Pooja back as much as Pooja had left.
Pooja then gave Neha as back as many euros as Neha had left, which left Pooja broke and gave Neha a total of 80 pounds. How much did Pooja and Neha have at the beginning of their exchange?

John and Jacob are planning on a vacation. John says, “It will be better if we take the train to the hotel. We will reach faster.”
To this, Jacob says, “No. You are wrong. The train stops halfway to the hotel and then we will have to walk the rest of the way. We should take the bikes to the hotel directly.”
John says, “You are wrong.”

Now, John takes the train while Jacob takes the bike. The train travels at four times the speed of the bike. The bike travels at twice the speed of walking.

Who do you think will reach the hotel first?