Question

4. In a three-digit number, the digit at the hundreds place is three times the digit at the ones place,
and the sum of the digits is 15. If the digits are reversed, the number is reduced by 396. Find the number​

Answer 1

Answer:

Here's the solution

Hope it helps

Answer 2

The number is 672.

Given:

• In a three-digit number, the digit at the hundreds place is three times the digit at the ones place,
• The sum of the digits is 15.
• If the digits are reversed, the number is reduced by 396.

To find:

• Find the number.

Solution:

Step 1:

Let the three digit number is xyz.

here x is hundreds place digit, y is tens place and z is at unit place.

ATQ.

$\bf x=3z...eq1$

and

$\bf x + y + z = 15...eq2$

and

Number in extended form:$100x + 10y + z$

Reverse number is in extended form: $100z + 10y + x$

Difference of both is 396.

$100x + 10y + z - 100z - 10y - x = 396$

or

$99x - 99z = 396$

or

$\bf x -z = 4...eq3$

Step 2:

Put value of eq1 in eq3

$3z - z = 4$

or

$2z = 4$

or

$\red{z = 2}$

put value of z in eq3.

$x - 2 = 4$

or

$\red{x = 6 }$

put value of x and z in eq2.

$6 + y + 2 = 15$

or

$y = 15 - 8$

or

$\red{y = 7}$

Thus,

The number is 672.

Verification:

672-276=396

Hence verified.

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