| A number divided by 13 leaves a remainder 1 and if the quotient, thus obtained, is divided by 5, we get remainder 3. What will be the remainder if the number is divided by 65? |
A) 28
B) 16
C) 18
D) 40
Correct Answer: D
Solution :
| Let the number be x and quotient be y. |
| \[\therefore \] \[\frac{x}{13}=y\frac{1}{3}\]\[\Rightarrow \]\[x=13y+1\] |
| Now, quotient is divided by 5 and remainder is 3 |
| \[\therefore \] \[\frac{y}{5}=1\frac{3}{5}\] |
| \[\Rightarrow \] \[y=5\times 1+3=8\] |
| \[\therefore \] \[x=13\times 8+1=104+1=105\] |
| Hence, remainder after dividing by 65 = 40 |
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