In a number of two digits, unit’s digit is twice the tens digit. If 36 be added to the number, the digits are reversed. The number is [1] (a) 36 (b) 63 (c) 48 (d) 84
Answers
If 36 be added to the number, the digits are reversed and the unit’s digit is 2 times the ten’s digit, then the number is option (c): 48.
Step-by-step explanation:
Let the unit’s digit be “y” and the ten’s digit be “x”, so, the number will be “(10x + y)”.
Case 1:
It is given that the unit’s digit is twice the ten’s digit, therefore, we get
y = 2x ……. (i)
Case 2:
Also given that, when 36 is added to the number (10x + y), then the digits are reversed to “(10y + x)”, therefore, we get
[10x + y] + 36 = 10y + x
⇒ 9x – 9y + 36 = 0
Substituting y = 2x from eq. (i)
⇒ 9x – (9*2x) = - 36
⇒ 9x – 18x = - 36
⇒ - 9x = -36
⇒ x = 4
∴ y = 2x = 2*4 = 8
Thus,
The number is = (10*4) + 8 = 40 + 8 = 48
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Answer:
If 36 be added to the number, the digits are reversed and the unit’s digit is 2 times the ten’s digit, then the number is option (c): 48.
Step-by-step explanation:
Let the unit’s digit be “y” and the ten’s digit be “x”, so, the number will be “(10x + y)”.
Case 1:
It is given that the unit’s digit is twice the ten’s digit, therefore, we get
y = 2x ……. (i)
Case 2:
Also given that, when 36 is added to the number (10x + y), then the digits are reversed to “(10y + x)”, therefore, we get
[10x + y] + 36 = 10y + x
⇒ 9x – 9y + 36 = 0
Substituting y = 2x from eq. (i)
⇒ 9x – (9*2x) = - 36
⇒ 9x – 18x = - 36
⇒ - 9x = -36
⇒ x = 4
∴ y = 2x = 2*4 = 8
Thus,
The number is = (10*4) + 8 = 40 + 8 =48