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. 240
• B. 270
• C. 295
• D. 360

Answer 1

The Correct Option is B

The solution involves using the relationship between dividends, divisors, quotients, and remainders in division along with the information given about the difference of the two numbers.

Let the larger number be x and the smaller number be y.

According to the problem:

• The difference between the numbers is 1365: \(x - y = 1365\).
• When the larger number is divided by the smaller, the quotient is 6 and the remainder is 15.
  So, we have \(x = 6y + 15\).

We now have two equations:

1. Equation 1: \(x - y = 1365\)
2. Equation 2: \(x = 6y + 15\)

To find the values of x and y, substitute Equation 2 into Equation 1:

\((6y + 15) - y = 1365\)

Simplify:

\(6y + 15 - y = 1365\)

\(5y + 15 = 1365\)

Subtract 15 from both sides:

\(5y = 1350\)

Divide both sides by 5:

\(y = 270\)

Thus, the smaller number is 270.