The sum of the digits of a two digit number is 12.if the digits are reversed, the new number is 4/7times the original number. Find the number.
Answers
Answer:
84
Step-by-step explanation:
suppose, the tens digit number be x.
the ones digit number be (12-x)
original number = 10×x + (12-x)
= 9x + 12
reversed number = 10(12 - x) +x
= 120 - 9x
A/Q
(9x + 12) × 4/7 = 120 - 9x
36x + 48 = 840 - 63x
99x = 792
x = 8
original number = 9x + 12
= 9×8 +12
= 84
EXPLANATION.
Let the tens place be = x
Let the unit place be = y
original number = 10x + y
reversed number = 10y + x
Case = 1.
The sum of digit of two digit number is 12
=> x + y = 12 ......(1)
Case = 2.
If the digit are reversed,the new number is
4/7 times the original number.
=> 10y + x = 4/7 ( 10x + y)
=> 7 ( 10y + x) = 4 ( 10x + y)
=> 70y + 7x = 40x + 4y
=> 66y = 33x
=> 2y = x ...... (2)
put the value of equation (2) in equation (1)
we get,
=> 2y + y = 12
=> 3y = 12
=> y = 4
put the value of y = 4 in equation (1)
we get,
=> x = 2 X 4 = 8
Therefore,
original number = 10x + y
=> 10 X 8 + 4 = 84