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प्रश्न
A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
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उत्तर
Let the ten's digit be x and the one's digit be y.
The number will be 10x + y
Given, a product of digits is 24
∴ xy = 24
or, y = `24/x` ...(i)
Given that when 18 is subtracted from the number, the digits interchange their places.
∴ 10x + y – 18 = 10y + x
or, 9x – 9y = 18 ...(ii)
Substituting y from equation (i) in equation (ii), we get
`9x - 9 (24/x)` = 18
or, `x - 24/x` = 2
or, x2 – 24 – 2x = 0
or, x2 – 2x – 24 = 0
or, x2 – 6x + 4x – 24 = 0
or, x(x – 6) + 4(x – 6) = 0
or, (x – 6)(x + 4) = 0
or, x – 6 = 0 and x + 4 = 0
or, x = 6 and x = −4
Since, the digit cannot be negative, so, x = 6
Substituting x = 6 in equation (i), we get
y = `24/6` = 4
∴ The number = 10(6) + 4 = 60 + 4 = 64
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