# Tough Maths problem

This is a very tough question.

Try this and see if you can solve it without using algebra.

Andy, Betty, Candy and Danny each have some money.

The amount of money Andy has is 1/3 of the total amount of money Betty, Candy and Danny have. The amount of money Betty has is 1/4 of the total amount of money Andy, Candy and Danny have. The amount of money Candy has is 1/5 of the total amount of money Andy, Betty and Danny have. If Danny has \$1725, how much do they have altogether?

Here’s the solution.

Step 1: Observe that if Andy has 1/3 of the amount of money as the rest, then the total must be divisible by 4 parts (so that Andy gets 1/4 and the rest gets 3/4.)

Step 2: Similarly, if Betty gets 1/4 of the rest, then the total must be divisible by 5 parts (so that she gets 1/5 and the rest gets 4/5). Similarly, the total is also divisible by 6 parts so that Candy gets 1/6 of the total.

Step 3: We need a number of units to represent the total. This number must be divisible by 4, 5 and 6. The smallest number for that is 60.

Step 4: Andy has 1/4 of the total, so that is 15 units (1/4 * 60 = 15). Betty has 1/5 of the total, so that is 12 units (1/5 * 60 = 12). Candy has 1/6 of the total, and that is 10 units (1/6 * 60 = 10). This means that Danny has 23 units (60-15-12-10 = 23).

Step 5: 23 units is \$1725. 1 unit is \$75. They have altogether 60 units = 60 * \$75 = \$4500.