A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.
Answers
SOLUTION :
Let the two digit number be 10x + y
Given : product of its digits(xy) = 8
xy = 8...................(1)
When 18 is subtracted from the number, the digits interchange their places
10x + y - 18 = 10y + x
10x + y - 10y - x = 18
9x - 9y = 18
9(x - y) = 18
x - y = 18/9
x - y = 2
x = 2 + y……………….(2)
Put this value of x in eq 1.
xy = 8
(2 + y)y = 8
2y + y² = 8
y² + 2y - 8 = 0
y² + 4y - 2y - 8 = 0
[By middle term splitting]
y(y + 4) - 2(y + 4) = 0
(y - 2 ) ( y + 4) = 0
(y - 2 ) = 0 or ( y + 4) = 0
y = 2 or y = - 4
Since, a digit can't be negative, so y ≠ - 4.
Therefore , y = 2
Put this value of y in eq 1,
xy =8
x× 2 = 8
x = 8/2 = 4
x = 4
Required number = 10x + y
= 10(4) + 2
= 40 + 2
Required number = 42
Hence, the Required two digit number is 42.
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Answer :
42
Step-by-step explanation :
Let the digit at unit's place be x and tens place be y.
∴ Original number = 10x + y
According to the question ;
Product of numbers is 8.
⇒ xy = 8 ...... (i)
When 18 is subtracted from the number, the digits interchange their places.
⇒ 10x + y - 18 = 10y + x
⇒ 10x - y - 10y - x = 18
⇒ 9x - 9y = 18
⇒ 9 ( x - y ) = 18
⇒ x - y = 2
⇒ x = 2 + y ..... (ii)
Putting the value of (ii) in eqⁿ (i),
xy = 8
⇒ y ( 2 + y ) = 8
⇒ 2y + y² = 8
⇒ y² + 2y - 8 = 0
⇒ y² + 4y - 2y - 8 = 0
⇒ y ( y + 4 ) - 2 ( y + 4 ) = 0
⇒ ( y + 4 ) ( y - 2 ) = 0
⇒ ( y + 4 ) = 0 or ( y - 2 ) = 0
⇒ y = - 4 or y = 2
Since, the digits cannot be in the negative form, hence the value of y = 2.
Putting the value of y in eqⁿ (ii),
x = 2 + y
⇒ x = 2 + 2
⇒ x = 4
Therefore, the number is ;
Original number = 10x + y
= 10 * 4 + 2
= 40 + 2
= 42
Hence, the required number is 42.