Ex 2.4, 3 Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?Let original number be ab
Let the digit at tens place = a
& digit at units place = b
Given that
Sum of digits of a 2-digit number = 9
a + b = 9
b = 9 a
Original Number
ab
Digit at units place = b = 9 a
Digit at tens place = a
Original number
= (10 Digit at tens place) + (1 Digit at units place)
= (10 a) + (1 (9 a))
= 10a + 9 a
= 9a + 9
Reverse number
ba
Digit at units place = a
Digit at tens place = b = 9 a
Resulting number
= (10 Digit at tens place) + (1 Digit at units place)
= 10 (9 a) + (1 a)
= 90 10a + a
= 90 9a
Hence,
Original number = 9a + 9
Resulting number = 90 9a
Given that,
Resulting number is greater than original number by 27.
Resulting number = Original number + 27
(90 9a) = (9a + 9) + 27
90 9a = 9a + 9 + 27
90 27 9 = 9a + 9a
54 = 18a
54/18 = a
3 = a
a = 3
Therefore,
Digit at tens place = a = 3
& Digit at units place = b = 9 a = 9 3 = 6
Hence,
Original number = 36

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.