The certain number of two digits is four times the sum of its digits and if 18 be added to it the digits will be reversed.Find the number?
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The certain number of two digits is four times the sum of its digits and if 18 be added to it the digits will be reversed.Find the number?
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Step-by-step explanation:
Let the tens digit of the number be x
And ones digit of the number = y
The original number = 10x + y
The revered number = 10y + x
According to the 1st condition:-
The number is four times the sum of its digits.
→ 10x + y = 4( x + y)
→ 10x + y = 4x + 4y
→ 10x - 4x + y - 4y = 0
→ 6x - 3y = 0
→ 2x - y = 0......(i)
According to the 2nd condition:-
If 18 be added to the original number the digits will be reversed.
→ 18 + 10x + y = 10y + x
→ 10x - x + y - 10y = -18
→ 9x - 9y = -18
→ x - y = -2.......(ii)
Subtracting equation (ii) from (i)
→ (2x - y) - ( x - y) = 0- (-2)
→ 2x + y - x + y = 2
→ x = 2
Substituting x = 2 in equation (ii)
→ x - y = -2
→ 2 - y = -2
→ -y = -2 - 2
= y = 4
The original number
= 10x + y
= 10(2) + 4
= 20 + 4
= 24
Hence:
Let x be units digit and y be the 10s digit
10y+x = 4(x+y)
10y + x = 4x +4y
6y-3x = 0
2y - x = 0 ————-(1)
When 18 is added to the number
10y + x +18 = 10x + y
Simplify
9y - 9x = -18
y - x = - 2
y = x - 2 —————-(2)
Substitute in equation #1
2(x-2) - x = 0
2x - 4 - x=0
x = 4
Substitute in equation#2
y = 2
There for the number is
2 x 10 + 4 = 24
So , the answer is 24.