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Answer:
35
Step-by-step explanation:
10x+y=3+6(x+y)
4x-5y=3(i)
10y+x+18=10x+y
9y-9x=-18
y-x=-2(ii)
(i)+4(ii)=-5=-y
y=5 x=3
35
Step-by-step explanation:
(3)
Let the ten's digit be x and the unit's digit be y respectively.
Required number = (10x + y).
According to the given condition,
10x + y = 6(x + y) + 3
⇒ 10x + y = 6x + 6y + 3
⇒ 10x + y - 6x - 6y = 3
⇒ 4x - 5y = 3
(ii)
If digits are reversed, the new number is 18 less than original.
⇒ 10y + x = (10x + y) - 18
⇒ 10y + x - 10x - y = -18
⇒ -9x + 9y = -18
⇒ 9x - 9y = 18
⇒ x - y = 2
On solving (i) & (ii) * 4, we get
⇒ 4x - 5y = 3
⇒ 4x - 4y = 8
-----------------
-y = -5
y = 5
Substitute y = 5 in (i), we get
⇒ 4x - 5y = 3
⇒ 4x - 25 = 3
⇒ 4x = 28
⇒ x = 7
Thus, Original number = 10x + y = 75
(4)
Let the digit in one's place be x and tens place be y.
Original number = 10y + x.
Number formed by reversing the digit = 10x + y.
(i)
According to the given condition,
10y + x = 8(x + y)
⇒ 10y + x = 8x + 8y
⇒ 10y + x - 8x - 8y = 0
⇒ -7x + 2y = 0
⇒ 7x - 2y = 0
(ii)
According to the give condition,
10y + x = 2(10x + y) + 18
⇒ 10y + x = 20x + 2y + 18
⇒ 10y + x - 20x - 2y = 18
⇒ -19x + 8y = 18
⇒ 19x - 8y = -18
On solving (i) * 4 & (ii), we get
28x - 8y = 0
19x - 8y = -18
----------------------
9x = 18
x = 2
Substitute y = 2 in (ii), we get
19x - 8y = -18
⇒ 19(2) - 8y = -18
⇒ 38 - 8y = -18
⇒ y = 7
∴ Thus, Original number = 10y + x = 72
Hope it helps!