Choose the correct option.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 beOptions3, 24, 12, 31, 2

To solve this problem, we can use the concept of the Chinese Remainder Theorem.

Let's denote the unknown number as x. According to the given information, when x is divided by 4, the remainder is 1, and when x is divided by 5, the remainder is 4.

Using the Chinese Remainder Theorem, we can find a unique solution for x modulo 20 (since 4 and 5 are coprime).

To find the solution, we can start by finding the inverse of 4 modulo 5. The inverse of 4 modulo 5 is 4 itself, since 4 * 4 ≡ 1 (mod 5).

Now, we can calculate x modulo 20 using the formula: x ≡ (1 * 5 * 4 + 4 * 4 * 1) ≡ 20 (mod 20)

Therefore, x ≡ 20 (mod 20). This means that x leaves a remainder of 20 when divided by 20.

Now, let's consider the second part of the question. We need to find the remainders when x is successively divided by 5 and 4.

Since x ≡ 20 (mod 20), we can write x as x = 20 + 20k, where k is an integer.

When x is divided by 5, the remainder will be 20k.

When x is divided by 4, the remainder will be 20k + 20 = 20(k + 1).

Therefore, the respective remainders when x is successively divided by 5 and 4 are both 20.

Hence, the correct option is 3.