Mohit will write such a two digit number that 4 times of the sum totalof the twi digit will be 3 more of the number and if the digits are reversed the number will be increasedby 18.calculate the number
Answers
The number is 13.
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]
According to the question, we can write the first equation as,
4 × [x + y] = 3 + [10x + y]
⇒ 4x + 4y = 3 + 10x + y
⇒ 3 + 6x - 3y = 0
⇒ 6x - 3y + 3 = 0
dividing throughout by 3
⇒ 2x - y + 1 = 0 ..... (i)
Now,
After reversing the digits, the new no. becomes = [10y + x]
According to the question the second equation can be written as,
[10y + x] = [10x + y] + 18
⇒ 10x - x + y - 10y + 18 = 0
⇒ 9x - 9y + 18 = 0
dividing throughout by 9
⇒ x - y + 2 = 0 ..... (ii)
Subtracting eq. (ii) from (i), we get
2x - y + 1 = 0
x - y + 2 = 0
- + -
-------------------
x - 1 = 0
------------------
∴ x = 1
Substituting the value of x in eq. (ii), we get
x - y + 2 = 0
⇒ 1 - y + 2 = 0
⇒ 3 - y = 0
⇒ y = 3
Thus,
The number is,
= 10x + y
= (10 × 1) + 3
= 10 + 3
= 13
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