Question

The difference between a three digit number and the number formed by reversing its first two digits is 450. If the sum of the number is 10. Determine the number

Answer 1

check the attachment

Answer 2

The three digit numbers may be 613 or 721.

Given:

• The difference between a three digit number and the number formed by reversing its first two digits is 450.
• If the sum of the number is 10.

To find:

• Determine the number.

Solution:

Concept to be used:

• Assume all three digits of number.
• Form equation by extended form of number.
• Solve both equations and find the number.

Step 1:

Let the digits of number are x,y, and z from left to write.

So,

The number may be written as

$100x + 10y + z$

The number obtained by reversing first two digits are

$100y + 10x + z$

ATQ,

$100x + 10y + z - 100y - 10x - z = 450$

or

$90x - 90y = 450$

or

$\bf x - y = 5...eq1$

Step 2:

Form another equation by adding it's digits.

$\bf x + y + z = 10...eq2$

Now analyse the eq1 and eq2 to find the numbers.

Case 1:

Difference between first two terms are 5,

Thus, first two terms may be 6 and 1

so, last digit will be 3.

Thus,

Number will be 613.

Verification:

613-163= 450

Case 2:

Thus, first two terms may be 7 and 2

so, last digit will be 1.

Thus,

Number will be 721.

Verification:

721-271=450

Case 3:

Thus, first two terms may be 5 and 0

so, last digit will be 5.

Thus,

Number will be 505.

Verification:

505-050≠450

Thus,

The three digit numbers may be 613 or 721.

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