A no. of consisting of two- digits is 7times the sum of its digits . When 27 is subtracted from the no. the digits are reversed. Find the no.
Answers
Answer:
The two digit number is 63
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to find: the number.
Step-by-step explanation:
As the number is a two digit , then let x be tens's place and y be one's place. Therefore the two digit number would form as 10 x +y
according to the question,
a number consisting of two digits is 7 times the sum of its digits.
=> 10 x + y = 7( x+y)
=> 3x-6y=0
=> x = 2y ..........................................(1)
when 27 is subtracted from the number the digits are reversed.
After reversing the digits, the number = 10 y +x
=> (10 x+ y )- 27 = 10y + x
=> 9 x- 9y = 27
=>x -y = 3 ........................(2)
Substituting the value of x from eq (1) to eq(2) , we get
=> 2y-y = 3
=> y = 3
x= 2y
=> x = 2(3) = 6
Therefore the number is = 10 (6) + 3 = 63
Answer : the required two digit number is 63
Sᴏʟᴜᴛɪᴏɴ :-
Let us Assume That, the original Number is (10x + y).
So,
→ 10x + y = 7(x + y)
→ 10x + y = 7x + 7y
→ 10x - 7x = 7y - y
→ 3x = 6y
→ x = 2y -------------- Eqn.(1)
Now,
→ Oringinal Number - 27 = Reversed .
→ Oringinal Number - Reversed = 27
→ (10x + y) - (10y + x) = 27
→ 10x - x + y - 10y
→ 9x - 9y = 27
→ 9(x - y) = 27
→ (x - y) = 3
Putting value of Eqn.(1) Now,
→ (2y - y) = 3
→ y = 3.
Therefore,
→ x = 2*3 = 6
Hence,
→ The original Number = 10x + y = 10*6 + 3 = 60 + 3 = 63(Ans.)