Question

A number when divided successively by 4 and 5 leaves remainder 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: For this type of problem we have to solve by writing the above sentences into mathematical forms and then step by step solving to obtain the remainder. We have to use Dividend = Divisor \[\times \]Quotient + Remainder.

Complete step-by-step solution -
Let the number be X.
When you divide X by 4 it gives remainder 1.
Let the divisor 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 divided Y completely.
\[Y=1\times 5+4=9\]
Putting Y in (1) we get the equation as follows,
\[X=4\times 9+1=37\]
The number 37 when divided by 5 and 4 leaves the remainder
\[37=5\times 7+2\]. . . . . . . . . . . . . . . (a)
\[7=4\times 1+3\]. . . . . . . . . . . . . . . . . . (b)
From the above we can conclude that the answer is option B.

Note: From (a) and (b) we can say that 37 when divided by 5 we get the quotient as 7 and when 7 divided by 4 we get remainder 3. To solve this type of problem care should be taken because in the question the numbers are just interchanged which leads us to put the option as D.