Question

A difference between two numbers is 1365, when larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. What is the smaller number?

• A. 240
• B. 360
• C. 270
• D. 295

Answer 1

The Correct Option is C

Let the smaller number be denoted by x and the larger number be denoted by y. According to the problem, we have two conditions:

• The difference between the two numbers is 1365. Thus, we can write:
  y - x = 1365
• When the larger number is divided by the smaller number, the quotient is 6 and the remainder is 15. This can be expressed by the equation:
  y = 6x + 15

Now, we have a system of two equations:

1. y = x + 1365
2. y = 6x + 15

We can set the right sides of these equations equal to each other:
x + 1365 = 6x + 15

Rearrange the terms to isolate x:
1365 - 15 = 6x - x
1350 = 5x

Now solve for x by dividing both sides by 5:
x = 1350 / 5
x = 270

Therefore, the smaller number is 270.