Find the number abcd, knowing that adding this number to the sum of the two numbers ab and cd gives 3740

Let's break down the problem step by step.

We are given that the number abcd can be written as 1000a + 100b + 10c + d.

We are also given that adding this number to the sum of the two numbers ab and cd gives 3740. Mathematically, this can be represented as:

1000a + 100b + 10c + d + (10a + b) + (10c + d) = 3740

Simplifying the equation, we have:

1010a + 101b + 20c + 2d = 3740

Dividing both sides of the equation by 2, we get:

505a + 505b + 10c + d = 1870

Now, let's analyze the equation further. We know that a, b, c, and d are all digits between 0 and 9. Since the left side of the equation is divisible by 5, the right side (1870) must also be divisible by 5.

The only possible values for a, b, c, and d that satisfy this condition are:

a = 3, b = 7, c = 4, d = 0

Therefore, the number abcd is 3740.