Question

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively, when it is successively divided by 5 and 4, then the respective remainders will be
A . 1,2
B . 2,3
C . 3,2
D . 4,1

Answer 1

Hint:  In order to solve this problem, assume a variable and divide it by 4 and leave the remainder 1. Then divide the dividend by 5 and leave the remainder 4.
Then solve the equation to get the answer.

Complete step by step solution:
Let the number be X.
When you divide X by 4, it gives the remainder 1.
Let the dividend here be Y
⇒X = 4Y+1 ...(1)
Now, when we divide Y by 5, we get remainder 4.
We take quotient as 1, as 5 divides Y completely.
⇒Y=1×5+4=9
Putting Y = 9 in equation (1), we get
X = 4×9+1 = 37
Now, 37 divided by 5 and 4 respectively will give 2 and 3.
Hence, the correct option is B.

Note: In these types of problems we always have to assume the variables and solve the problem according to the question asked. Most importantly keep in mind that you should never assume an integer and mark the option correct, as there can be more possible options .