Gujjubhai has forget the ATM pin number of his debit card What he remembers is the following hints ...... Let's see how many of you can help him out 1) it's 4 digit number 2) 1st digit is Half of 3rd digit 3) 2nd and 3rd digit total is 8 4) 4th digit equals to multiplication of 1st and 2nd digit. 5) summation of all 4 digit equals to 12 Find out the Atm pin number
Answers
Answer:
4080
Step-by-step explanation:
let the four digits be written as;
a b c d
Now as per given information, we can formulate some equations
2) 1st digit is Half of 3rd digit
c = 2 a
3) b + c = 8
4) a x b = d
a + b + c + d = 12
If we now apply some hit and trial technique, we find that below numbers satisfy the above equations,
a = 4
b = 0
c = 8
d = 0
4080
The ATM pin number is 4 0 8 0
Step-by-step explanation:
Let the ATM pin number be a b c d
Instruction 1 ⇒ a = c/2 → (equation 1)
Instruction 2 ⇒ b + c = 8 → (equation 2)
b = 8 - c → (equation 5)
Instruction 3 ⇒ ab = d → (equation 3)
Instruction 4 ⇒ a + b + c + d = 12 → (equation 4)
On substituting equation (1), (2) and (3) in equation (4), we get,
⇒ c/2 + 8 + ab = 12
⇒ c/2 + 8 + (c/2 × (8 - c)) = 12
⇒ c/2 + 8 + 4c - c²/2 = 12
⇒ c/2 - c²/2 + 4c = 4
⇒ c - c² + 8c = 8
⇒ 9c - c² - 8 = 0
⇒ c² - 9c + 8 = 0
⇒ (c - 8)(c - 1) = 0
⇒ c = 8 or 1
When "c = 1" is substituted in equation (1) then the value of a is in decimal which is not possible.
∴ c = 8
From equation (1) ⇒ a = 8/2 = 4
From equation (5) ⇒ b = 8 - 8 = 0
From equation (3) ⇒ d = 4 × 0 = 0
Thus, a b c d = 4 0 8 0