Question

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and 15 as remainder. What is the smaller number ?

• A. 270
• B. 240
• C. 295
• D. 360

Answer 1

The correct option is A

270

Let the smaller number be $x.$
$\Rightarrow$ Larger number = $x+1365$
By Euclid's division lemma, the larger number can also be written as $6x+15.$
$\Rightarrow x+1365=6x+15$
$\Rightarrow 5x=1350$
$\Rightarrow x=270$

$\therefore$ The smaller number is 270 and the larger number is 270 + 1365 = 1635.