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If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order, we get 4 as a quotient and 3 as a remainder. If we divide the
required number by the sum of its digits, we get 8 as a quotient and 7 as a remainder.
Find the number?
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If we divide the unknown two-digit number by the number consisting of ...
Solution:

Given Data:
- Quotient when the two-digit number is divided by the number consisting of the same digits written in reverse order = 4
- Remainder when the two-digit number is divided by the number consisting of the same digits written in reverse order = 3
- Quotient when the number is divided by the sum of its digits = 8
- Remainder when the number is divided by the sum of its digits = 7

Let's assume the unknown two-digit number is represented by 10x + y, where x and y are the digits of the number.

Dividing the unknown number by its reverse:
- The number consisting of the same digits written in reverse order = 10y + x
- Given, (10x + y) ÷ (10y + x) = 4 with a remainder of 3

Equation 1:
10x + y = 4(10y + x) + 3
=> 10x + y = 40y + 4x + 3
=> 6x = 39y + 3
=> 2x = 13y + 1

Dividing the number by the sum of its digits:
- The sum of the digits = x + y
- Given, (10x + y) ÷ (x + y) = 8 with a remainder of 7

Equation 2:
10x + y = 8(x + y) + 7
=> 10x + y = 8x + 8y + 7
=> 2x = 7y + 7
=> 2x = 7(y + 1)

Solving Equations 1 and 2 simultaneously:
2x = 13y + 1
2x = 7(y + 1)
From the above two equations, we get:
13y + 1 = 7(y + 1)
=> 13y + 1 = 7y + 7
=> 6y = 6
=> y = 1
Substitute y = 1 in Equation 1:
2x = 13(1) + 1
=> 2x = 14
=> x = 7
Therefore, the two-digit number is 71.
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If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order, we get 4 as a quotient and 3 as a remainder. If we divide therequired number by the sum of its digits, we get 8 as a quotient and 7 as a remainder.Find the number?
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