The sum of the digits of a unit of a two-digit number and the sum of the digits of the decimal is equal to 16, if we subtract 53 from the number. Find the number by forming equations. Ans 97.
Answers
Answer:let the unit place digit be x and tens place digit be y
then the two-digit number will be 10y + x
and the number formed by interchanging the unit place and tens place digits will be 10x + y
according to the first condition given in the qs i.e, the sum of two numbers is 110 that is
10y + x + 10x + y = 110
=> 11x + 11y = 110
divide the above equation by 11 we get
x + y = 10
x = 10 - y ....(i)
now according to the second equation,
if 10 is subtracted from the first number i.e, the new number is 10y + x - 10
given that the new number is 4 more than 5 time the sum of its digits in the first number i.e
the sum of its digits in the first number is x + y, now 5 times of its, 5(x + y), and now 4 more that is, 4 + 5(x + y)
therefore new number = 4 + 5(x + y)
10y + x - 10 = 4 +5(x + y)
10y - 5y + x = 4 +10 +5x
5y = 14 + 4x.....(ii)
substitute the value of x from eq(i) to eq (ii)
we get , 5y = 14 + 4(10 - y)
5y = 14 + 40 - 4y
y = 6
and from eq(i)
x = 4
then the first number 10y + x = 10x6 + 4 = 64
first number is 64.
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