Question

A 3-digit number is such that the unit digit, tens digit and hundreds digit are in the ratio 1:2:3. The sum of this number and its reversed number is 1332. Find the number

• A. 890
• B. 928
• C. 980
• D. 963

Answer 1

Answer:

D. 963

The required 3-digit number is 963.

• Define the digits using the ratio:
  The ratio of the units, tens, and hundreds digits is given as 1:2:3.
  Let the units digit ($u$) be $x$.
  The tens digit ($t$) becomes $2x$.
  The hundreds digit ($h$) becomes $3x$.

• Express the original and reversed numbers:

  • Original Number = $100h + 10t + u = 100(3x) + 10(2x) + x = \mathbf{321x}$

  • Reversed Number = $100u + 10t + h = 100(x) + 10(2x) + 3x = \mathbf{123x}$

• Set up the sum equation:
  $\text{Original} + \text{Reversed} = 1332$
  $321x + 123x = 1332$
  $444x = 1332$

• Solve for $x$:
  $x = \frac{1332}{444} = \mathbf{3}$

• Find the digits:

  • Units digit = $x = \mathbf{3}$

  • Tens digit = $2x = 2 \times 3 = \mathbf{6}$

  • Hundreds digit = $3x = 3 \times 3 = \mathbf{9}$

Combining these digits gives the original number, 963.