In a 3 digit number, the difference of hundred's digit and unit's digit is 5. Find the quotient when difference of 3-digit number and number obtained by reversing the digits is divided by 9
Answers
Answer:
Step-by-step explanation:
a 3 digit number, the difference of hundred's digit and unit's digit is 5
To find : the quotient when difference of 3-digit number and number obtained by reversing the digits is divided by 9
Solution:
3 digit number ABC
A - C = 5
Reversed number CBA
ABC Value = 100A + 10B + C
CBA Value = 100C + 10B + A
Difference = 100A + 10B + C - (100C + 10B + A)
= 100(A - C) + C - A
= 100(A-C) -(A -C)
= 99(A-C)
= 99 * 5
= 9 * 11 * 5
= 9 * 55
divided by 9 Hence Quotient = 55
Answer :
›»› The quotient when difference of 3-digit number and number obtained by reversing the digits is divided by 9 is 55.
Given :
- A 3 digit number, the difference of hundred's digit and unit's digit is 5.
To Find :
- The quotient when difference of 3-digit number and number obtained by reversing the digits is divided by 9.
Solution :
Let us assume that, the number in 100's place is "x", the number in 10's place is "y", and the number in 1's place is "z" respectively.
Original number = 100x + 10y + z.
Reverse of number = 100x + 10y + z.
Difference of digit in 100's place and 1's place is 5.
→ x - z = 5 ........(1)
Difference of original number and reverse of number.
→ 100x + 10y + z - (100z + 10y + x)
→ 100x + 10y + z - 100z - 10y - x
Cancelling 10y,
→ 100x + z - 100z - x
→ 100x - x - 100z - z
→ 99x - 100z - z
→ 99x - 99z
Taking 9 as common,
→ 99(x - z)
From equation (1),
→ x - z = 5
→ 99 * 5
→ 9 * 11 * 5
So, the quotient when divided by 9,
→ (9 * 11 * 5) / 9
9 and 9 cancel out,
→ 11 * 5
→ 55
Hence, the quotient when difference of 3-digit number and number obtained by reversing the digits is divided by 9 is 55.