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Mkey [24]
3 years ago
5

A two digit number becomes 5/6 of the reversed number when the digits are interchanged the difference between the digits is 1 fi

nd the number.
Friends plz helpe plz plz plz
I want answer with full explanation
I will mark him as brainliest​

Mathematics
1 answer:
Rina8888 [55]3 years ago
4 0

Answer:

Original number = 54

Reversed number = 45

Step-by-step explanation:

Let the tens place digit be x and unit's place digit be y.

Therefore, required no. = 10x + y

Number obtained after interchanging the digits = 10y + x

According to the given condition:

10y+ x =  \frac{5}{6} (10x + y) \\ 6(10y + x) = 5(10x + y) \\ 60y + 6x = 50x + 5y \\ 60y + 6x - 50x - 5y = 0 \\ 55y - 44x = 0 \\ 11(5y - 4x) = 0 \\ 5y - 4x = 0.....(1) \\ according \: to \: the \: second \: condition \\ x - y = 1 \\ x = y + 1....(2) \\ from \: equations \: (1) \: and \: (2) \\ 5y - 4(y + 1) = 0 \\ 5y  - 4y  - 4= 0\\ y  - 4  = 0 \\ y  =  4 \\ substituting \: y =  4 \: in \: equation \: (2) \\ x =  4 + 1 \\ x =  5 \\  \\ 10x + y = 10 \times 5 + 4 = 50 + 4 = 54 \\ 10y + x = 10 \times 4 + 5 = 40 + 5 = 45 \\

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