The difference between the two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. Find the smallest number?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 270
In a division, dividend = divisor × quotient + remainder. With the smaller number \(S\) as the divisor, the larger number is \(6S+15\); the difference of the two numbers gives an equation in \(S\).
Larger number: \(L=6S+15\) (1)
Difference: \(L-S=1365\) (2)
Putting (1) in (2): \(5S+15=1365\)
\(5S=1350\), so \(S=270\)