A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will beOptions4, 12, 31, 23, 2

To solve this problem, let's start by finding the number that satisfies the given conditions.

We know that when the number is divided by 4, the remainder is 1. This means that the number can be written as 4a + 1, where 'a' is an integer.

Next, when the number is divided by 5, the remainder is 4. So, we can write the number as 5b + 4, where 'b' is an integer.

Now, let's find the number that satisfies both conditions. We can equate the two expressions:

4a + 1 = 5b + 4

Simplifying this equation, we get:

4a - 5b = 3

To find the values of 'a' and 'b' that satisfy this equation, we can use trial and error or apply the Euclidean algorithm. By trying different values, we find that a = 4 and b = 3 satisfy the equation.

Therefore, the number can be written as:

4a + 1 = 4(4) + 1 = 17

Now, we need to find the remainders when this number is successively divided by 5 and 4.

When 17 is divided by 5, the remainder is 2. So, the first option is 2.

When 17 is divided by 4, the remainder is 1. So, the second option is 1.

Therefore, the correct answer is 2, 1.