The sum of a two digit number and the number formed by interchanging its digits is 110.if 10 is subtracted from the first number,the new number is 4 more than 5 times the sum of the digits in the first number .find the first number.
Answers
Answer:
64
Step-by-step explanation:
Let's say the ones digit number be x and tens digit number be y.
So, the original number is 10y + x and interchanged number is 10x + y.
The sum of a two digit number and the number formed by interchanging its digits is 110.
As per given statement,
→ 10y + x + 10x + y = 110
→ 11x + 11y = 110
→ x + y = 10
→ x = 10 - y
Also, said that if 10 is subtracted from the first number
→ 10y + x - 10
The new number is 4 more than 5 time the sum of its digits in the first number.
→ 4 + 5(x + y)
Therefore,
→ 10y + x - 10 = 4 + 5(x + y)
→ 10y - 5y + x = 4 + 10 + 5x
→ 5y = 14 + 4x
Substitute value of x above
→ 5y = 14 + 4(10 - y)
→ 5y = 14 + 40 - 4y
→ 5y + 4y = 54
→ 9y = 54
→ y = 6
Substitute value of y in x
→ x = 10 - 6
→ x = 4
Therefore, the first number = 10y + x = 10(6) + 4 = 64