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  • A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Answers (1)

Solution:
Let the first digit = x
Let the ten’s digit = y
Therefore the number = 10y + x
As per the question
8(x + y) –5 = 10y + x
8x + 8y – 10y – x = 5
7x – 2y = 5 … (1)
16(y – x) + 3 = 10y + x
16y – 16x – 10y – x = – 3
–17x + 6y = –3
17x – 6y = 3 … (2)
Multiply equation (1) by 3
21x – 6y = 15
17x – 6y = 3
–        +     –
4x = 12
x = 3
Put x = 3 in eq. (1)
7(3) –2y = 5
–2y = 5 –21

y = \frac{16}{2} = 8
Hence the number is = 10y + x = 10(8) + 3 = 83
 

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